What is the largest 4-digit number that is equal to the cube of the sum of its digits?

Question

Algebra level question

Answer 1

5832=(5+8+3+2)^3.

Comments

The method used is to first calculate the largest 4-digit perfect cube. To do this take the cube root of 9999=21.5 approx., so 21^3=9261 is the largest cube, but the sum of the digits is 18. 20^3=8000, sum of digits=8; 19^3=6859, sum of digits=28; 18^3=5832, sum of digits=18. Bingo!

Answer 2

The number we seek, in particular, is a 4-digit cube. Thus, we can start with the largest 4-digit cube, and work our way down.


The largest 4-digit cube is , but .


The next lowest cube is , but .


The next lowest cube is , but .


The next lowest cube is , and , so the answer is .