Bumbletown had the most robbed bank in the land. The unfortunate clerk was frequently forced to open the safe, and the bank had lost so much money, that Mr Good, the bank manager, was going bald.
Then one day, Mr Good had an idea. His nephew, Fumble, should be the bank clerk. Now Fumble was the ideal man for the job. His memory was so bad, one could be sure that no robber could ever force him to remember the safe combination. Furthermore, his poor powers of recall were matched by a superb talent for puzzling things out. This meant that whenever Fumble needed to know the safe combination, all he had to do was obtain the following conundrum from Mr Good, which he could solve to reveal the five-digit safe combination.
‘The fourth digit is four greater than the second digit. There are three pairs of digits that each sum to 11. The third of the five digits is three less than the second. The first digit is three times the fifth digit.’
Of the 100,000 possible numbers, which was the correct safe combination?
The correct combination is 65292.
Since the third digit is three less than the second, and the fourth is four greater than the second, there are only three possible combinations for the second, third and fourth digits. These are -307-, -418-, and -529-.
With the first digit three times the fifth, the only possible combinations for the first and fifth digits are 0 0,3 1, 6 2, and 9 3. The solution arises from combining these two sets of possibilities, with the added criteria that there are three combinations of two digits that that each sum to 11.