Here is a new sort of number puzzle we hope you will enjoy. They were invented by Whit McMahan and are similar to his Balance Quest puzzles, but with some new twists. These are great puzzles just for relaxing, but we also think they would make good tools to use in the classroom. Puzzlers are required to add and subtract positive and negative numbers as well as exercise their powers of deduction.
Here are the rules for filling out a small grid Checkerboard:
- Fill in the 16 darker grey boxes with the integers 1 to 8 and -1 to -8. (Some of them will already be filled in to get you started). You must use all sixteen possible numbers, so you can use only one of each. It helps if you make a list of all sixteen numbers and then cross them off as you use them.
- The lighter boxes boxes may contain some of the same numbers as the darker grey boxes, but they can contain no repeats amongst themselves.
- Now comes the addition. Numbers that appear in a box between two other boxes must equal the sum of the numbers in the adjacent boxes. This applies vertically as well as horizontally. For example, you can see in the sample solution that the first set of three vertical boxes gives us the addition 8 + (-6) = 2.
The rules for the larger grids are the same, except you use the integers 1 to 16 and -1 to -16 to complete the dark grey squares.
To solve the puzzle fill in any additions you know straight off. As you fill in some numbers, new additions will become evident. Once you have done all of the obvious additions, it is time to use your powers of deduction. Try the remaining possibilities for the dark grey squares, considering that you must use one example of each of the numbers 1 to 8 and -1 to -8 (or 1 to 16 and -1 to -16 for the larger puzzles). There is only one possible solution.
To introduce you to the Checkerboard puzzle, Whit has given us some puzzles that you can print out and enjoy. Be sure to visit his website Balance Quest Puzzle for more puzzles and to order his book.
Print the Puzzles
Each set of puzzles has the solution included.