Question 1198924
<font color=black size=3>
Hint:


1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
Focus on the units digit of each result to get this sequence: 1, 4, 9, 6, 5, 6, 9, 4, 1
Notice we have symmetry.


Sort the values and toss out any duplicates to get: 1, 4, 5, 6, 9


-------------------------------------------------------


Another hint:


Q = P+1 since PP and PQ are consecutive numbers (eg: 64 and 65)
PP and PQ are of different parity (one is odd, the other even, in either order)
(PP)^2 and (PQ)^2 are of different parity. I'll leave the proof for the reader.


odd + even = odd
which means QRQR is odd, and R itself is odd
The possible values of R is from the set {1,3,5,7,9}
</font>