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Lesson 3

1. Lesson 3

1.6. Explore 5

Mathematics 30-3 Module 2

Module 2: Number

 

Often when solving a puzzle, you will make a mistake. The mistake may show itself as you continue to solve the puzzle. In Try This 3, you will try to determine where a mistake occurred in a solution.

 

Try This 3

 

A nonogram is a puzzle where you try to shade in the correct spaces in a grid to reveal a picture. The numbers on the outside of the grid tell you how many blocks there are in each row or column, and how these are grouped.

 

 

This diagram shows a 6 by 6 nonogram puzzle. The clue for the last row is a 3. The last row shows a blank, filled, filled, filled, blank, then blank square.

 

 

This diagram shows a 6 by 6 nonogram puzzle. The clue for the third row is a 2.1. The third row shows a filled, filled, blank, blank, filled, then blank square.

 

 

This diagram shows a 6 by 6 nonogram puzzle. The clue for the second column is a 2 on top of a 1. The second column shows a blank, blank, filled, filled, blank, then filled square.

 

Faiza is going to solve the nonogram shown.

 

 

This diagram shows a 6 by 6 nonogram puzzle. The clues for the rows are 1, 5, 1.1.1, 1, 1.1, 1.1. The clues for the columns are 2, 1.2, 4, 1.2, 2, 0.

 

She begins to complete the puzzle, as shown, using an x in boxes she knows cannot be filled. In step 6, she realizes that it is impossible to use the clue 1.1.1 because she has already concluded that the red box cannot be used.

 

 

This illustration shows 6 steps in solving a 6 by 6 nonogram. The nonogram when completed will have the following characteristics: � Row 1 has 1 block of length 1 coloured. � Row 2 has 1 block of length 5 coloured. � Row 3 has 3 blocks each of length 1 coloured. � Row 4 has 1 block of length 1 coloured. � Row 5 has 2 blocks each of length 1 coloured. � Row 6 has 2 blocks each of length 1 coloured. � Column 1 has 1 block of length 2 coloured. � Column 2 has 2 blocks, one of length 1 and one of length 2 coloured. � Column 3 has 1 block of length 4 coloured. � Column 4 has 2 blocks, one of length 1 and one of length 2 coloured. � Column 5 has 1 block of length 2 coloured. � Column 6 has no blocks coloured. In the first step, the 6th column has had x placed in each square, since they must be blank. In step 2, the 5 remaining squares in row 2 are filled in to give the block of length 5. In step 3, row 1 column 5 is coloured In step 4, the remaining squares in row 2 are marked with an x as are the remaining squares in column 5. In step 5, the squares in column 3 that are shared with rows 3, 4, and 5 are coloured. In step 6, the squares in row 3 that are shared with columns 1 and 5 are filled in. The column 5 square already has an x and is coloured in red.

  1. Follow Faiza’s steps and determine in which step her error occurred. Explain how you know an error occurred.
  2. Complete the puzzle correctly.
  3. Describe how you could make your own nonogram puzzle for another student to complete.

 course folder Save your responses in your course folder.

 

In Try This 3, an error occurred in step 3. Faiza did not have enough information to conclude that the square should be filled in. When solving puzzles of this type, it is important to be entirely sure before filling in a box with a square or an x.