7^2=49 < 50 < 8^2=64 < 9^2=81 < 10^2=100 < 110 < 11^2=121
so there are 3 perfect squares greater than 50 and less than 100 viz. 64, 81 and 100.
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To start you off here's a hint: 144 = 122...
The perfect squares less than 101 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.
Answer: 1, 64, & 729
1, 4, 9, 16 and 25.