Thinking and Problem Solving: Apply It

  • Explain how we use concepts, prototypes, and schema to organize information
  • Understand the difference between natural and artificial concepts
  • Describe common problem-solving strategies

Everyday Connections: Solving Puzzles

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

Typically, a Sudoku puzzle is a 9×9 grid. The simple Sudoku below (Figure 1) is a 4×4 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 see how you do!

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.
Figure 1. How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Connect the Dots

Here is another popular type of puzzle that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.
Figure 2. Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, it will be hard to forget.

Puzzling Scales

Take a look at the “Puzzling Scales” logic puzzle below (Figure 3). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”
Figure 3. The puzzle reads, “Since the scales now balance…and balance when arranged this way, then how many marbles will it require to balance with that top?

What problem-solving method could you use to solve Einstein’s famous riddle?

You can view the transcript for “Can you solve “Einstein’s Riddle”? – Dan Van der Vieren” here (opens in new window).