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This week's quiz is a set of brain twisters.
1. Twenty different numbers are written on 10 pieces of paper, one on either side (front and back) of each piece. The sum of two numbers on each paper piece is always the same and the sum of all ten numbers on the visible side of the paper pieces (shown below) equals the sum of the ten numbers on the hidden side (back side). What number should replace the question mark?
| 36 | 5 | 24 | ? | 2 | 31 | 42 | 35 | 17 | 21 |
2. Use each of the digits from 0 to 8 to fill the blanks in the given equation, so that the equation holds true. No digit can be used more than once. The 4 shown is to denote x to the power 4.
____ ____ 4 = ____ ____ ____ ____ ____ ____ ____
3. The 9 x 9 square below lists 81 digits. Find a continuous path of 10 digits, each in a different square that adds up to the highest total and another path that adds up to the lowest total. The path may proceed horizontally and vertically but not diagonally. What is the highest and lowest total?
| 3 | 1 | 4 | 1 | 5 | 9 | 2 | 6 | 5 |
| 3 | 5 | 8 | 9 | 7 | 9 | 3 | 2 | 3 |
| 8 | 4 | 6 | 2 | 6 | 4 | 3 | 3 | 8 |
| 3 | 2 | 7 | 9 | 5 | 0 | 2 | 8 | 8 |
| 4 | 1 | 9 | 7 | 1 | 6 | 9 | 3 | 9 |
| 9 | 3 | 7 | 5 | 1 | 0 | 5 | 8 | 2 |
| 0 | 9 | 7 | 4 | 9 | 4 | 4 | 5 | 9 |
| 2 | 3 | 0 | 7 | 8 | 1 | 6 | 4 | 0 |
| 6 | 2 | 8 | 6 | 2 | 0 | 8 | 9 | 9 |
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