Monthly Archives: August 2017

Answer to STEP I 2007 Q.1

I/2007/1 – A positive integer with 2n digits (the first of which must not be 0) is called a balanced number if the sum of the first n digits equals the sum of the last n digits. For example, 1634 is a 4-digit balanced number, but 123401 is not a balanced number. (i) Show that seventy 4-digit balanced numbers can be made using the digits 0, 1, 2, 3 and 4. (ii) Show that \frac{1}{6}k(k+1)(4k+5) 4-digit balanced numbers can be made using the digits 0 to k. You may use the identity \sum_1^n{r^2} \equiv \frac{1}{6}n(n+1)(2n+1) Continue reading