A game involves guessing a fivedigit number Ten points are a

A game involves guessing a five-digit number. Ten points are awarded for each correctly placed digit, and one additional point for each digit that would be correctly placed when the expression rearranged to make the highest possible score. Find the number that would be worth 55 points if 34567 is worth 2 points, 13579 is worth 13 points, 42160 is worth 1 point and 33515 is worth 33 points. Copies of the Problem of the Month may be obtained from Mrs. Potty Kennedy. MNS Building Give worked solutions back to her by May 4^th if you have any Questions see Or. Bruce Burdick. MNS 233 Anyone may submit a solution The correct solutions will be divided into two piles; \'RWU Students\' and \"Others\" One solution will be randomly drawn from each pile The winner will receive a T-SHIRT!

Solution

Use 33515, which has 3 correct digits in correct positions, to find the 5 choose 3 = 10 possible forms for the correct solution.

Then use 34567, which has 2 correct digits in incorrect positions to isolate the form a3b15. This also eliminates 4, 6, and 7 as solution digits.

Then use 42160, which has one correct digit in an incorrect position (1), to eliminate 0 and 2 as solution digits.

Finally use 13579, which has three correct digits, one of which is in the correct position while two are not, to eliminate 9 as a solution digit.

Thus, both a and b must be 8, so the solution is 83815.