Rounded Roots


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
32mapsradical32 maps 5.6568542...maps6

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?


5.52 = 30.25, so radical30 less than 5.5 and 6.52 = 42.25, so radical43 > 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?

Problem ID: 47 (May 2001)     Difficulty: 2 Star

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