Regions

Number Theory Level 1

Is it possible to place every one of the following numbers \[1^2,\ 2^2,\ 3^2,\ 4^2,\ 5^2,\ \dots,\ 25^2,\ 26^2,\ 27^2\] into either of the two regions \(A\) and \(B\) below such that the sums of the numbers in each region are equal?