Who is asking: Parent
Level: Middle
Question:
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.
Thanks!
Hi,
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.
Penny