There are many sets of two different positive integers a and b, both less than 50, such that a^{2} and b^{2} end in the same last two digits. For example, 35^{2}=1225 and 45^{2}=2025 both end in 25. What are all possible values for the average of a and b?
For the purposes of this problem, single-digit squares are considered to have a leading zero, so for example we consider 2^{2} to end with the digits 04 , not 4.