Quandaries and Queries


Who is asking: Parent
Level: Middle

What is the 5 digit number in which the first 2 digits are the square of the 3rd digit and the last 2 digits are the square of the digit that is one less than the third digit? The sum of all the digits is 22.




I think this is essentially a "guess and check" problem. The middle digit, and one less than the middle digit, are digits that have a square that is a two digit number. The possible choices for this middle digit are then 5, 6 ,7, 8 and 9. Thus there are only five possibilities for your 5 digit number. Construct them and see which one has 22 as the sum of its digits.

For example if the middle digit is 9 then the number is 81964. The sum of the digits is

8 + 1 + 9 + 6 + 4 = 28.

This is too big so the middle digit must be one of the other four.



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