Question

The product of three consecutive non-zero integers is 3333 times the sum of the three integers. What is the sum of the digits of this product

Answer 1

x(x + 1)(x + 2) = 3,333(x + x + 1 + x + 2)

x(x² + 3x + 2) = 3,333(3x + 3)

x³ + 3x² + 2x = 9,999x + 9,999

x³ + 3x² - 9,997x - 9,999 = 0

x = 99, so x + 1 = 100 and x + 2 = 101

99 × 100 × 101 = 999,900

The sum of the digits in this product is 36.