Easier than It Looks

Number Theory Level 2

There are four three digit natural numbers that satisfy the condition that each the sum of the cubes of its digits.

Here are the three of these numbers:

$\begin{aligned} 153&=&1^3+5^3+3^3 \\ 370&=&3^3+7^3+0^3 \\ 407&=&4^3+0^3+7^3 \\ \end{aligned}$

Can you find the remaining missing number?

1 solution

Devin Ky
May 16, 2015

We are given that 370 = 3^3 + 7^3 + 0^3 = 3^3 + 7^3. Adding 1 to both sides, 370 + 1 = 3^3 + 7^3 + 1 , Thus 371 = 3^3 + 7^3 + 1^3.

No wonder easier than it looks!!! 83% cannot solve. It seems that many cannot seem to think simply when the time calls for it. :[

Noel Lo - 6 years ago

I have also solved the problem using the same method.

Muhammad Mahdi Shahriar Sakib - 6 years ago