Select the number that best completes the analogy: 16 : 2 :: 81 : ?

The relation is a number : the number whose fourth power it is. Since $2\times 2\times 2\times 2=16$, the first term hides a fourth root, and $3\times 3\times 3\times 3=81$ gives 3. The strong trap is 9, the square root of 81, which fits the far commoner square-root pattern but fails on the first pair, where the square root of 16 is 4 and not 2. 27 is 81 ÷ 3 and 4 is the square root of 16 quoted in the wrong place.