Alex has before him some positive whole numbers, each consisting of a single digit, which may be repeated. The digit is different for each number, and the number of times it is repeated is also different for each number.
The sum of Alex's numbers is a number in which each digit is larger than the digit on its left, and it is the largest number for which this is possible, given the constraints described above.
What is the sum of Alex's numbers?
Note: Adapted from Enigma number:1765 which appeared on "New Scientist" in 2013.
Either Alex's sum is 3 digits or more than 3 digits.
Suppose it is 3 digits.
Then the number of repeated digits is 1,2,and 3.
The largest 3 digit number with strictly incrreasing digits is 789, but this is 777 + 12; and 12 is 11 + 1 which re-uses a digit. Next is 689 which is 666 + 23; and 23 is 22 + 1.
So we have our solution, unless there is a way for number with more than 3 digits: 1 + 22 + 666 = 689.
Still need to prove that having a 4-digit number will fail to generate a sum with strictly increasing digits.
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Posted by Larry
on 2024-05-28 18:06:56 |
Partial analytic solution
