Question

The number 111…111 (100 ones) is multiplied by 101. The resulting number is then also multiplied by 101. The number obtained in the second step is again multiplied by 101. What is the sum of the digits of the number obtained in the third step?

Answer 1

800

Explanation:

The three multiplication steps are equivalent to multiplying by ...

101³ = 1030301

The sum of digits of the product will be the sum of digits of the partial products, since none of the digit-by-digit multiplications results in a product that is more than 10.

The sum of digits of the third product is ...

(1 × 100) × (1 + 3 + 3 + 1) = 800