Square sum
One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
Age
14 to 16
Challenge level
Problem
One of the following is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
A. 118
B. 128
C. 138
D. 148
E. 158
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 148
110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118
or 120 + ... + 128
etc
sum = 9$\times$ middle number
114$\times$9
124$\times$9
134$\times$9
144$\times$9 = 12$^2\times$3$^2$ = (12$\times$3)$^2$ so is a square number