Originally Posted by

**Soroban** Hello, aznmartinjai!

With a little *thinking*, you can narrow down the choices.

Since the number is between 100 and 200, the first digit is "1".

The other digits must be odd: 1, 3, 5, 7, 9

But 7³ = 343 and 9³ = 729 . . . too large.

So the number is comprised of 1s, 3s, and/or 5s.

If the number has no 5s, the largest is 133 . → . 1³ + 3³ + 3² .= .55

. . Hence, the number contains one 5.

There are only four choices: 115, 135, 151, 153.

. . 115 . → . 1³ + 1³ + 5³ .= .127

. . 135 . → . 1³ + 3³ + 5³ .= .153

. . 151 . → . 1³ + 5³ + 1³ .= .127

. . 153 . → . 1³ + 5³ + 3³ .= .153 . ← .There!