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Digits 1 Solution

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I’m thinking of a 3-digit number. If I add its three digits together I get 26. What numbers could I possibly be thinking of?

Solution

First we need to know what the three digits could be. What three digits when added together give a total of 26?

If one of the digits is 7 then the other three add to 26 – 7 = 19. But 2 × 9 = 18, so no two digits can add to 19. So none of the original digits is 7. In fact none of them is smaller than 7 for the same reason.

They can't all be 9 (3 × 9 = 27 > 26), so I must have one 8 and two 9s.

So, what numbers can be made up with one 8 and two 9s? There are just three of them. They are 998, 989, and 899.

Extension

Make up some problems like this to try on your friends. You could start off with 2- or 3-digits numbers.