Study the analogy 6 : 64 :: 9 : ? and choose the missing number.

The number is raised by 2 and the result is squared. For 6 that is $8\times 8=64$; for 9 it is $11\times 11=121$. The trap 81 squares the number as it stands, but 6 squared is 36 and not 64. 100 raises the number by only 1 before squaring, which on the first pair gives 49, and 144 raises it by 3, which gives 81 the first time.