The Puzzle: Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight 'dots' .4.5.6.7.8.9.0. which would add up to 82
To solve the puzzle and find a way to arrange the seven figures (4, 5, 6, 7, 8, 9, 0) and the eight dots ('.'), which would add up to 82, we can follow a step-by-step approach:
1. Start by identifying the two numbers that need to be placed as the first and second digits in the sequence. Since we want the sum to be 82, the highest possible two-digit number we can form is 98. Therefore, place the digits 9 and 8 in the first two spots, respectively.
2. Next, find the remaining five numbers (3 figures and 2 dots) that should sum up to 82 minus 98, which is -16. Since we have a negative sum, we need to distribute these numbers carefully to balance the equation.
3. Notice that it is not possible to add up any combination of the remaining five numbers and get -16 without making the equation unbalanced or exceeding the allowed number of digits. Therefore, it is not possible to arrange the figures and dots in a way that would add up to 82.
Hence, we can conclude that there is no solution to this puzzle.