# cubes of their digits

There are four numbers that are equal to the sum of the cubes of their digits.  Below are three of them.

What is the missing equation?

153 = 1 cubed + 5 cubed + 3 cubed
370 = 3 cubed + 7 cubed + 0 cubed
?
407 = 4 cubed + 0 cubed + 7 cubed

### 3 guesses to cubes of their digits

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• Matt

I started to try to figure this out using some mathematical method. However, I finally noticed that to get 370, the last added “cube” was adding a 0 to the number. Thus, you can both increment the left side and right side of the equation by adding a 1 (1 and 1 cubed, respectively). Thus,

371 = 3 cubed + 7 cubed + 1 cubed

BTW, thanks for putting these out there every day. They are a lot of fun to try to solve.

• Matt, you are today’s winner!
371. 3 cubed + 7 cubed + 1 cubed.