Find three consecutive odd whole numbers such that the sum of their squares is a four-digit number whose digits are all the same.

Source: mathcontest.olemiss.edu 7/16/2007

**SOLUTION
**Let be an odd whole number. Then, form three consecutive odd numbers.

**Sum of squares
**

Since is odd, is odd. If is odd, then is odd and if is odd, then is odd. So we will try different four-digit odd numbers starting from 1111, 3333, 5555, etc.

**Guess and check
**

Not a solution because is a whole number.

Not a solution.

**Check
**

**Answer**: 41, 43, 45.

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