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Answers to 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 |
The number in the '?' square will be 37. The sum of the two numbers on each piece is 50 and the total of all the 10 pieces of paper is 250.
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.
__3__ __2__ 4 = _1___ __0__ _4___ _8___ __5__ __7__ __6__
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?
The highest total path is shown in blue and the lowest total path is shown in red. The highest total is 80 and the lowest total is 16.
| 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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