mathschallenge.net

Problem

A special number machine will accept any whole number, find its square root and then output the result rounded off to the nearest whole number.
For example,

Input				Output
32		32 5.6568542...		6

If the output is 6, one possible input is 32, but which other numbers could have gone into the machine to give an output of 6?

Solution

5.5² = 30.25, so 30 5.5 and 6.5² = 42.25, so 43 > 6.5.

Hence the solution set is 31, 32, 33, ..., 42

Find the solution sets for each of the integers from 1 to 10.

Is there a rule connecting the output with the solution set?