Math CentralQuandaries & Queries


Question from Maria, a parent:

This is my son's homework. He is 7. Can you help?

Sue has a favourite number.
It is an even number.
It has 3 digits.
The digits add up to 15.

Find 10 numbers that could be Sue's number?

Hi Maria,

Since the number is even its units digit must be even, that is 0, 2, 4, 6, or 8. Suppose the units digit is 8 then the sum of the other two digits is $15 - 8 = 7.$ Find two digits which have a sum of $7.$ That gives you a number that could be Sue's favourite. Find another two digits which have a sum of $7.$ Remember that if the sum of two digits is $7$ you can switch their order and the sum is still $7.$ Watch out that your son doesn't make the hundreds digit of Sues favourite digit a $0,$ because then it is really a two digit number.

Once you have found some possibilities consider numbers where the units digit is $6.$ In this case what is the sum of the other two digits?

I hope this helps,

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