# Sum Of Digits is 43 Puzzle - Solution

## The Puzzle:

I am thinking of a 6-digit number. The sum of the digits is 43.

And

(1) it's a square number,

(2) it's a cube number, and

(3) the number is under 500000.

And

**only two**of the following three statements about the number are true:(1) it's a square number,

(2) it's a cube number, and

(3) the number is under 500000.

## Our Solution:

Only Statements 1 and 3 are true. The number is 499849.

707

499849<500000

707

^{2}= 499849499849<500000