We seek a number n such that, when n is divided by each of the divisors 2,3,4,5...10, the remainder is one less than the divisor. This means that the number n +1 is exactly divisible by each of these numbers without a reminder and so n +1 is a multiple of all the numbers 2,3,4,5,...10. The smallest value of n +1 with the required property is 2x3x3x4x5x7=2520 so the smallest value of n is 2519.

A correct solution was received from Heacham Middle School.