{"id":513,"date":"2020-05-27T18:24:05","date_gmt":"2020-05-27T18:24:05","guid":{"rendered":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/?post_type=chapter&#038;p=513"},"modified":"2021-09-13T15:38:47","modified_gmt":"2021-09-13T15:38:47","slug":"problem-solving-2","status":"publish","type":"chapter","link":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/chapter\/problem-solving-2\/","title":{"raw":"Problem Solving","rendered":"Problem Solving"},"content":{"raw":"<div class=\"PageContent-ny9bj0-0 iapMdy\">\r\n<div id=\"main-content\" class=\"MainContent__HideOutline-sc-6yy1if-0 bdVAq\">\r\n<div id=\"a5032008-aa12-4360-992a-2741ba0b3a73\">\r\n<div id=\"3614\" class=\"ui-has-child-title\"><section>\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">Learning Objectives<\/span><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"3614\" class=\"ui-has-child-title\"><section>By the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Describe problem solving strategies<\/li>\r\n \t<li>Define algorithm and heuristic<\/li>\r\n \t<li>Explain some common roadblocks to effective problem solving and decision making<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<span style=\"font-size: 1em;text-align: initial\">People face problems every day\u2014usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.<\/span><\/section><\/div>\r\n<section id=\"fs-idm10771072\">\r\n<h3>Problem-Solving Strategies<\/h3>\r\n<p id=\"fs-idm55655984\">When you are presented with a problem\u2014whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.<\/p>\r\n<p id=\"fs-idm81082576\">A\u00a0<strong><span id=\"term463\">problem-solving strategy<\/span><\/strong>\u00a0is a plan of action used to find a solution. Different strategies have different action plans associated with them (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Table_07_03_01\">Table LI.2<\/a>). For example, a well-known strategy is\u00a0<strong><span id=\"term464\">trial and error<\/span><\/strong>. The old adage, \u201cIf at first you don\u2019t succeed, try, try again\u201d describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn\u2019t work, you could check to make sure the paper tray isn\u2019t jammed. Or maybe the printer isn\u2019t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.<\/p>\r\n\r\n<div id=\"Table_07_03_01\" class=\"os-table\">\r\n<table class=\"top-titled\" summary=\"Table 7.2 \">\r\n<thead>\r\n<tr>\r\n<th colspan=\"3\" scope=\"col\">Table LI.2 Problem-Solving Strategies<\/th>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"col\">Method<\/th>\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Example<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Trial and error<\/td>\r\n<td>Continue trying different solutions until problem is solved<\/td>\r\n<td>Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Algorithm<\/td>\r\n<td>Step-by-step problem-solving formula<\/td>\r\n<td>Instruction manual for installing new software on your computer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Heuristic<\/td>\r\n<td>General problem-solving framework<\/td>\r\n<td>Working backwards; breaking a task into steps<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">Another type of strategy is an algorithm. An\u00a0<\/span><strong style=\"text-align: initial;font-size: 1em\"><span id=\"term465\">algorithm<\/span><\/strong><span style=\"text-align: initial;font-size: 1em\">\u00a0is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?<\/span><\/p>\r\n<p class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">A <\/span><strong style=\"text-align: initial;font-size: 1em\">heuristic<\/strong><span style=\"text-align: initial;font-size: 1em\"> is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a\u00a0<\/span><span id=\"term466\" style=\"text-align: initial;font-size: 1em\">heuristic<\/span><span style=\"text-align: initial;font-size: 1em\">\u00a0is a general problem-solving framework (Tversky &amp; Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A \u201crule of thumb\u201d is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):<\/span><\/p>\r\n\r\n<\/div>\r\n<ul id=\"fs-idm24198944\">\r\n \t<li>When one is faced with too much information<\/li>\r\n \t<li>When the time to make a decision is limited<\/li>\r\n \t<li>When the decision to be made is unimportant<\/li>\r\n \t<li>When there is access to very little information to use in making the decision<\/li>\r\n \t<li>When an appropriate heuristic happens to come to mind in the same moment<\/li>\r\n<\/ul>\r\n<p id=\"fs-idm161874848\"><strong><span id=\"term467\">Working backwards<\/span><\/strong>\u00a0is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Halifax, Nova Scotia, and have been invited to a wedding at 4 PM on Saturday in Cape Breton. Knowing that the Canso Causeway can be backed up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 3 hours to get to Cape Breton without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.<\/p>\r\n<p id=\"fs-idm26711856\">Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.<\/p>\r\n&nbsp;\r\n\r\n<\/section><section id=\"fs-idm10771072\">\r\n<div id=\"fs-idp39443200\" class=\"psychology everyday-connection ui-has-child-title\"><header><strong><a id=\"TTheuristics\"><\/a>TRICKY TOPIC: HEURISTICS\r\n<\/strong>[embed]https:\/\/youtu.be\/MtvY54Pfr7M[\/embed]\r\n\r\n<em><span style=\"font-size: 1em;text-align: initial\">If the video above does not load, click here:\u00a0<a href=\"https:\/\/youtu.be\/MtvY54Pfr7M\">https:\/\/youtu.be\/MtvY54Pfr7M<\/a><\/span><\/em>\r\n\r\n<section id=\"fs-id1470001\"><span id=\"term70\"><em>For a full transcript of this video, click <a href=\"\/intropsychneuro\/back-matter\/appendix\/#heuristics\">here<\/a><\/em>\u00a0<\/span><\/section><\/header><section>\r\n<div class=\"os-note-body\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">EVERYDAY CONNECTION<\/span><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<h4 id=\"10406\" class=\"os-subtitle\"><span class=\"os-subtitle-label\">Solving Puzzles<\/span><\/h4>\r\n<p id=\"fs-idm81906192\">Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9\u00d79 grid. The simple sudoku below (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Sudoku\">Figure LI.7<\/a>) is a 4\u00d74 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.<\/p>\r\n\r\n<div id=\"Figure_07_03_Sudoku\" class=\"os-figure\">\r\n<figure>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img id=\"94787\" src=\"https:\/\/openstax.org\/resources\/01777a6ec1d560e341c4b2a872f4a72a25d502d9\" alt=\"A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.\" width=\"487\" height=\"487\" \/> Figure LI.7\u00a0How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-idp18699600\">Here is another popular type of puzzle (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_DotsAndLines\">Figure LI.8<\/a>) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:<\/p>\r\n\r\n<div id=\"Figure_07_03_DotsAndLines\" class=\"os-figure\">\r\n<figure>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"486\"]<img id=\"7906\" src=\"https:\/\/openstax.org\/resources\/949ef1107fff17aec65765441135ef5f62dcf1ba\" alt=\"A square shaped outline contains three rows and three columns of dots with equal space between them.\" width=\"486\" height=\"489\" \/> Figure LI.8\u00a0Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won\u2019t forget.[\/caption]<\/figure>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"Figure_07_03_DotsAndLines\" class=\"os-figure\">\r\n<h3 class=\"os-caption-container\"><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1em;font-weight: bold\">Pitfalls to Problem Solving<\/span><\/h3>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><section id=\"fs-idp55827040\">\r\n<p id=\"fs-idp83546720\">Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, \u201cInsanity is doing the same thing over and over again and expecting a different result.\u201d Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck\u2014but they just need to go to another doorway, instead of trying to get out through the locked doorway. A\u00a0<strong><span id=\"term468\">mental set\u00a0<\/span><\/strong>is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.<\/p>\r\n<p id=\"fs-idp7857216\"><strong><span id=\"term469\">Functional fixedness<\/span><\/strong>\u00a0is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Duncker\">Figure LI.10<\/a>). During the\u00a0<em>Apollo 13<\/em>\u00a0mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.<\/p>\r\n\r\n<div id=\"Figure_07_03_Duncker\" class=\"os-figure\">\r\n<figure>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"244\"]<img id=\"36511\" src=\"https:\/\/openstax.org\/resources\/bbe68e72de6eec39cffa48530b41d9714bfd92ab\" alt=\"Figure a shows a book of matches, a box of thumbtacks, and a candle. Figure b shows the candle standing in the box that held the thumbtacks. A thumbtack attaches the box holding the candle to the wall.\" width=\"244\" height=\"331\" \/> Figure LI.10\u00a0In Duncker's classic study, participants were provided the three objects in the top panel and asked to solve the problem. The solution is shown in the bottom portion.[\/caption]<\/figure>\r\n<\/div>\r\n<div id=\"fs-idp23754352\" class=\"psychology link-to-learning ui-has-child-title\"><section>\r\n<div class=\"os-note-body\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">LINK TO LEARNING<\/span><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">Check out this\u00a0<a href=\"http:\/\/openstax.org\/l\/Apollo13\" target=\"_blank\" rel=\"noopener nofollow\">Apollo 13 scene about NASA engineers overcoming functional fixedness<\/a>\u00a0to learn more.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<p id=\"fs-idp34596688\">Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German &amp; Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German &amp; Barrett, 2005).<\/p>\r\n<p id=\"fs-idm130151376\">In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let\u2019s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An\u00a0<strong><span id=\"term470\">anchoring bias\u00a0<\/span><\/strong>occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you\u2019re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.<\/p>\r\n<p id=\"fs-idm73967264\">The\u00a0<strong><span id=\"term471\">confirmation bias<\/span><\/strong>\u00a0is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behaviour exhibited by the professor while ignoring the countless pleasant interactions they are involved in on a daily basis.\u00a0<strong><span id=\"term472\">Hindsight bias<\/span><\/strong>\u00a0leads you to believe that the event you just experienced was predictable, even though it really wasn\u2019t. In other words, you knew all along that things would turn out the way they did.\u00a0<strong><span id=\"term473\">Representativeness heuristic\u00a0<\/span><\/strong>describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.<\/p>\r\n<p id=\"fs-idp35880832\">Finally, the\u00a0<strong><span id=\"term474\">availability heuristic<\/span><\/strong>\u00a0is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision<strong>.<\/strong>\u00a0Biases tend to \u201cpreserve that which is already established\u2014to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses\u201d (Aronson, 1995; Kahneman, 2011). These biases are summarized in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Table_07_03_02\">Table LI.3<\/a>.<\/p>\r\n\r\n<div id=\"Table_07_03_02\" class=\"os-table\">\r\n<table class=\"top-titled\" summary=\"Table 7.3 \">\r\n<thead>\r\n<tr>\r\n<th colspan=\"2\" scope=\"col\">LI.3 Summary of Decision Biases<\/th>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"col\">Bias<\/th>\r\n<th scope=\"col\">Description<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Anchoring<\/td>\r\n<td>Tendency to focus on one particular piece of information when making decisions or problem-solving<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Confirmation<\/td>\r\n<td>Focuses on information that confirms existing beliefs<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Hindsight<\/td>\r\n<td>Belief that the event just experienced was predictable<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Representative<\/td>\r\n<td>Unintentional stereotyping of someone or something<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Availability<\/td>\r\n<td>Decision is based upon either an available precedent or an example that may be faulty<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">LINK TO LEARNING<\/span><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><span style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\">Watch this\u00a0<\/span><a style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\" href=\"http:\/\/openstax.org\/l\/CogBias\" target=\"_blank\" rel=\"noopener nofollow\">teacher-made music video about cognitive biases<\/a><span style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\">\u00a0to learn more.<\/span><\/div>\r\n<\/div>\r\n<\/div>\r\n<h3>Inductive vs Deductive Reasoning<\/h3>\r\n<span style=\"font-size: 1em\">Scientific and everyday reasoning both employ\u00a0<\/span><strong style=\"font-size: 1em\">inductive reasoning<\/strong><span style=\"font-size: 1em\">: drawing general conclusions from specific observations. For example, a person\u2019s opinion that cramming for a test increases performance may be based on her own memory of passing an exam after pulling an all-night study session. Similarly, a researcher\u2019s conclusion\u00a0<\/span><em style=\"font-size: 1em\">against<\/em><span style=\"font-size: 1em\">\u00a0cramming might be based on studies comparing the test performances of people who studied the material in different ways (e.g., cramming versus study sessions spaced out over time). In these scenarios, both scientific and everyday conclusions are drawn from a limited\u00a0<\/span><span style=\"font-size: 1em\">sample<\/span><span style=\"font-size: 1em\">\u00a0of potential observations.<\/span><\/section><\/div>\r\n<strong>Deductive reasoning\u00a0<\/strong>starts with general principles that are applied to specific instances (the reverse of inductive reasoning). When the general principles, or\u00a0<em>premises<\/em>, are true, and the structure of the argument is valid, the conclusion is, by definition,\u00a0<em>proven;\u00a0<\/em>it must be so. A deductive truth\u00a0<em>must\u00a0<\/em>apply in all relevant circumstances. For example, all living cells contain DNA. From this, you can reason\u2014deductively\u2014that any specific living cell (of an elephant, or a person, or a snake) will therefore contain DNA. Given the complexity of psychological phenomena, which involve many contributing factors, it is nearly impossible to make these types of broad statements with certainty.\r\n<div id=\"a5032008-aa12-4360-992a-2741ba0b3a73\"><section id=\"fs-idp55827040\">\r\n<p id=\"fs-idm116954640\">Were you able to determine how many marbles are needed to balance the scales in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_SamLoyd\">Figure LI.9<\/a>? You need nine. Were you able to solve the problems in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Sudoku\">Figure LI.7<\/a>\u00a0and\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_DotsAndLines\">Figure LI.8<\/a>? Here are the answers (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Solutions\">Figure LI.11<\/a>).<\/p>\r\n\r\n<div id=\"Figure_07_03_Solutions\" class=\"os-figure\">\r\n<figure>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]<img id=\"39264\" src=\"https:\/\/openstax.org\/resources\/82ef427695b2fa200511f7ca6b80b7097a9b4536\" alt=\"The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle\u2019s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square\u2019s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.\" width=\"731\" height=\"387\" \/> Figure LI.11 Solutions to previous examples.[\/caption]<\/figure>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"PageContent-ny9bj0-0 iapMdy\">\n<div id=\"main-content\" class=\"MainContent__HideOutline-sc-6yy1if-0 bdVAq\">\n<div id=\"a5032008-aa12-4360-992a-2741ba0b3a73\">\n<div id=\"3614\" class=\"ui-has-child-title\">\n<section>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">Learning Objectives<\/span><\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"ui-has-child-title\">\n<section>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Describe problem solving strategies<\/li>\n<li>Define algorithm and heuristic<\/li>\n<li>Explain some common roadblocks to effective problem solving and decision making<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"font-size: 1em;text-align: initial\">People face problems every day\u2014usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.<\/span><\/section>\n<\/div>\n<section id=\"fs-idm10771072\">\n<h3>Problem-Solving Strategies<\/h3>\n<p id=\"fs-idm55655984\">When you are presented with a problem\u2014whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.<\/p>\n<p id=\"fs-idm81082576\">A\u00a0<strong><span id=\"term463\">problem-solving strategy<\/span><\/strong>\u00a0is a plan of action used to find a solution. Different strategies have different action plans associated with them (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Table_07_03_01\">Table LI.2<\/a>). For example, a well-known strategy is\u00a0<strong><span id=\"term464\">trial and error<\/span><\/strong>. The old adage, \u201cIf at first you don\u2019t succeed, try, try again\u201d describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn\u2019t work, you could check to make sure the paper tray isn\u2019t jammed. Or maybe the printer isn\u2019t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.<\/p>\n<div id=\"Table_07_03_01\" class=\"os-table\">\n<table class=\"top-titled\" summary=\"Table 7.2\">\n<thead>\n<tr>\n<th colspan=\"3\" scope=\"col\">Table LI.2 Problem-Solving Strategies<\/th>\n<\/tr>\n<tr>\n<th scope=\"col\">Method<\/th>\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Example<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Trial and error<\/td>\n<td>Continue trying different solutions until problem is solved<\/td>\n<td>Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning<\/td>\n<\/tr>\n<tr>\n<td>Algorithm<\/td>\n<td>Step-by-step problem-solving formula<\/td>\n<td>Instruction manual for installing new software on your computer<\/td>\n<\/tr>\n<tr>\n<td>Heuristic<\/td>\n<td>General problem-solving framework<\/td>\n<td>Working backwards; breaking a task into steps<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">Another type of strategy is an algorithm. An\u00a0<\/span><strong style=\"text-align: initial;font-size: 1em\"><span id=\"term465\">algorithm<\/span><\/strong><span style=\"text-align: initial;font-size: 1em\">\u00a0is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?<\/span><\/p>\n<p class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">A <\/span><strong style=\"text-align: initial;font-size: 1em\">heuristic<\/strong><span style=\"text-align: initial;font-size: 1em\"> is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a\u00a0<\/span><span id=\"term466\" style=\"text-align: initial;font-size: 1em\">heuristic<\/span><span style=\"text-align: initial;font-size: 1em\">\u00a0is a general problem-solving framework (Tversky &amp; Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A \u201crule of thumb\u201d is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):<\/span><\/p>\n<\/div>\n<ul id=\"fs-idm24198944\">\n<li>When one is faced with too much information<\/li>\n<li>When the time to make a decision is limited<\/li>\n<li>When the decision to be made is unimportant<\/li>\n<li>When there is access to very little information to use in making the decision<\/li>\n<li>When an appropriate heuristic happens to come to mind in the same moment<\/li>\n<\/ul>\n<p id=\"fs-idm161874848\"><strong><span id=\"term467\">Working backwards<\/span><\/strong>\u00a0is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Halifax, Nova Scotia, and have been invited to a wedding at 4 PM on Saturday in Cape Breton. Knowing that the Canso Causeway can be backed up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 3 hours to get to Cape Breton without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.<\/p>\n<p id=\"fs-idm26711856\">Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.<\/p>\n<p>&nbsp;<\/p>\n<\/section>\n<section>\n<div id=\"fs-idp39443200\" class=\"psychology everyday-connection ui-has-child-title\">\n<header><strong><a id=\"TTheuristics\"><\/a>TRICKY TOPIC: HEURISTICS<br \/>\n<\/strong><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Tricky Topics: Heuristics\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/MtvY54Pfr7M?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><em><span style=\"font-size: 1em;text-align: initial\">If the video above does not load, click here:\u00a0<a href=\"https:\/\/youtu.be\/MtvY54Pfr7M\">https:\/\/youtu.be\/MtvY54Pfr7M<\/a><\/span><\/em><\/p>\n<section id=\"fs-id1470001\"><span id=\"term70\"><em>For a full transcript of this video, click <a href=\"\/intropsychneuro\/back-matter\/appendix\/#heuristics\">here<\/a><\/em>\u00a0<\/span><\/section>\n<\/header>\n<section>\n<div class=\"os-note-body\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">EVERYDAY CONNECTION<\/span><\/p>\n<\/header>\n<div class=\"textbox__content\">\n<h4 id=\"10406\" class=\"os-subtitle\"><span class=\"os-subtitle-label\">Solving Puzzles<\/span><\/h4>\n<p id=\"fs-idm81906192\">Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9\u00d79 grid. The simple sudoku below (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Sudoku\">Figure LI.7<\/a>) is a 4\u00d74 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.<\/p>\n<div id=\"Figure_07_03_Sudoku\" class=\"os-figure\">\n<figure>\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"94787\" src=\"https:\/\/openstax.org\/resources\/01777a6ec1d560e341c4b2a872f4a72a25d502d9\" alt=\"A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.\" width=\"487\" height=\"487\" \/><figcaption class=\"wp-caption-text\">Figure LI.7\u00a0How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-idp18699600\">Here is another popular type of puzzle (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_DotsAndLines\">Figure LI.8<\/a>) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:<\/p>\n<div id=\"Figure_07_03_DotsAndLines\" class=\"os-figure\">\n<figure>\n<figure style=\"width: 486px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"7906\" src=\"https:\/\/openstax.org\/resources\/949ef1107fff17aec65765441135ef5f62dcf1ba\" alt=\"A square shaped outline contains three rows and three columns of dots with equal space between them.\" width=\"486\" height=\"489\" \/><figcaption class=\"wp-caption-text\">Figure LI.8\u00a0Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won\u2019t forget.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"os-figure\">\n<h3 class=\"os-caption-container\"><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1em;font-weight: bold\">Pitfalls to Problem Solving<\/span><\/h3>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<section id=\"fs-idp55827040\">\n<p id=\"fs-idp83546720\">Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, \u201cInsanity is doing the same thing over and over again and expecting a different result.\u201d Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck\u2014but they just need to go to another doorway, instead of trying to get out through the locked doorway. A\u00a0<strong><span id=\"term468\">mental set\u00a0<\/span><\/strong>is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.<\/p>\n<p id=\"fs-idp7857216\"><strong><span id=\"term469\">Functional fixedness<\/span><\/strong>\u00a0is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Duncker\">Figure LI.10<\/a>). During the\u00a0<em>Apollo 13<\/em>\u00a0mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.<\/p>\n<div id=\"Figure_07_03_Duncker\" class=\"os-figure\">\n<figure>\n<figure style=\"width: 244px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"36511\" src=\"https:\/\/openstax.org\/resources\/bbe68e72de6eec39cffa48530b41d9714bfd92ab\" alt=\"Figure a shows a book of matches, a box of thumbtacks, and a candle. Figure b shows the candle standing in the box that held the thumbtacks. A thumbtack attaches the box holding the candle to the wall.\" width=\"244\" height=\"331\" \/><figcaption class=\"wp-caption-text\">Figure LI.10\u00a0In Duncker&#8217;s classic study, participants were provided the three objects in the top panel and asked to solve the problem. The solution is shown in the bottom portion.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<div id=\"fs-idp23754352\" class=\"psychology link-to-learning ui-has-child-title\">\n<section>\n<div class=\"os-note-body\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">LINK TO LEARNING<\/span><\/p>\n<\/header>\n<div class=\"textbox__content\">Check out this\u00a0<a href=\"http:\/\/openstax.org\/l\/Apollo13\" target=\"_blank\" rel=\"noopener nofollow\">Apollo 13 scene about NASA engineers overcoming functional fixedness<\/a>\u00a0to learn more.<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<p id=\"fs-idp34596688\">Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German &amp; Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German &amp; Barrett, 2005).<\/p>\n<p id=\"fs-idm130151376\">In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let\u2019s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An\u00a0<strong><span id=\"term470\">anchoring bias\u00a0<\/span><\/strong>occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you\u2019re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.<\/p>\n<p id=\"fs-idm73967264\">The\u00a0<strong><span id=\"term471\">confirmation bias<\/span><\/strong>\u00a0is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behaviour exhibited by the professor while ignoring the countless pleasant interactions they are involved in on a daily basis.\u00a0<strong><span id=\"term472\">Hindsight bias<\/span><\/strong>\u00a0leads you to believe that the event you just experienced was predictable, even though it really wasn\u2019t. In other words, you knew all along that things would turn out the way they did.\u00a0<strong><span id=\"term473\">Representativeness heuristic\u00a0<\/span><\/strong>describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.<\/p>\n<p id=\"fs-idp35880832\">Finally, the\u00a0<strong><span id=\"term474\">availability heuristic<\/span><\/strong>\u00a0is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision<strong>.<\/strong>\u00a0Biases tend to \u201cpreserve that which is already established\u2014to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses\u201d (Aronson, 1995; Kahneman, 2011). These biases are summarized in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Table_07_03_02\">Table LI.3<\/a>.<\/p>\n<div id=\"Table_07_03_02\" class=\"os-table\">\n<table class=\"top-titled\" summary=\"Table 7.3\">\n<thead>\n<tr>\n<th colspan=\"2\" scope=\"col\">LI.3 Summary of Decision Biases<\/th>\n<\/tr>\n<tr>\n<th scope=\"col\">Bias<\/th>\n<th scope=\"col\">Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Anchoring<\/td>\n<td>Tendency to focus on one particular piece of information when making decisions or problem-solving<\/td>\n<\/tr>\n<tr>\n<td>Confirmation<\/td>\n<td>Focuses on information that confirms existing beliefs<\/td>\n<\/tr>\n<tr>\n<td>Hindsight<\/td>\n<td>Belief that the event just experienced was predictable<\/td>\n<\/tr>\n<tr>\n<td>Representative<\/td>\n<td>Unintentional stereotyping of someone or something<\/td>\n<\/tr>\n<tr>\n<td>Availability<\/td>\n<td>Decision is based upon either an available precedent or an example that may be faulty<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><span style=\"color: #ffffff\">LINK TO LEARNING<\/span><\/p>\n<\/header>\n<div class=\"textbox__content\"><span style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\">Watch this\u00a0<\/span><a style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\" href=\"http:\/\/openstax.org\/l\/CogBias\" target=\"_blank\" rel=\"noopener nofollow\">teacher-made music video about cognitive biases<\/a><span style=\"text-align: initial;font-family: Lora, serif;font-size: 1em;font-weight: normal\">\u00a0to learn more.<\/span><\/div>\n<\/div>\n<\/div>\n<h3>Inductive vs Deductive Reasoning<\/h3>\n<p><span style=\"font-size: 1em\">Scientific and everyday reasoning both employ\u00a0<\/span><strong style=\"font-size: 1em\">inductive reasoning<\/strong><span style=\"font-size: 1em\">: drawing general conclusions from specific observations. For example, a person\u2019s opinion that cramming for a test increases performance may be based on her own memory of passing an exam after pulling an all-night study session. Similarly, a researcher\u2019s conclusion\u00a0<\/span><em style=\"font-size: 1em\">against<\/em><span style=\"font-size: 1em\">\u00a0cramming might be based on studies comparing the test performances of people who studied the material in different ways (e.g., cramming versus study sessions spaced out over time). In these scenarios, both scientific and everyday conclusions are drawn from a limited\u00a0<\/span><span style=\"font-size: 1em\">sample<\/span><span style=\"font-size: 1em\">\u00a0of potential observations.<\/span><\/section>\n<\/div>\n<p><strong>Deductive reasoning\u00a0<\/strong>starts with general principles that are applied to specific instances (the reverse of inductive reasoning). When the general principles, or\u00a0<em>premises<\/em>, are true, and the structure of the argument is valid, the conclusion is, by definition,\u00a0<em>proven;\u00a0<\/em>it must be so. A deductive truth\u00a0<em>must\u00a0<\/em>apply in all relevant circumstances. For example, all living cells contain DNA. From this, you can reason\u2014deductively\u2014that any specific living cell (of an elephant, or a person, or a snake) will therefore contain DNA. Given the complexity of psychological phenomena, which involve many contributing factors, it is nearly impossible to make these types of broad statements with certainty.<\/p>\n<div>\n<section>\n<p id=\"fs-idm116954640\">Were you able to determine how many marbles are needed to balance the scales in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_SamLoyd\">Figure LI.9<\/a>? You need nine. Were you able to solve the problems in\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Sudoku\">Figure LI.7<\/a>\u00a0and\u00a0<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_DotsAndLines\">Figure LI.8<\/a>? Here are the answers (<a class=\"autogenerated-content\" href=\"https:\/\/openstax.org\/books\/psychology-2e\/pages\/7-3-problem-solving#Figure_07_03_Solutions\">Figure LI.11<\/a>).<\/p>\n<div id=\"Figure_07_03_Solutions\" class=\"os-figure\">\n<figure>\n<figure style=\"width: 731px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"39264\" src=\"https:\/\/openstax.org\/resources\/82ef427695b2fa200511f7ca6b80b7097a9b4536\" alt=\"The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle\u2019s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square\u2019s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.\" width=\"731\" height=\"387\" \/><figcaption class=\"wp-caption-text\">Figure LI.11 Solutions to previous examples.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":14,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":33,"_links":{"self":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapters\/513"}],"collection":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":19,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapters\/513\/revisions"}],"predecessor-version":[{"id":2135,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapters\/513\/revisions\/2135"}],"part":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/parts\/33"}],"metadata":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapters\/513\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/wp\/v2\/media?parent=513"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/pressbooks\/v2\/chapter-type?post=513"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/wp\/v2\/contributor?post=513"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/digitaleditions.library.dal.ca\/intropsychneuro\/wp-json\/wp\/v2\/license?post=513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}