Challenge Level

First download the Excel file .

Find sets of three numbers so that the sum of the squares of the first two is equal to the square of the third, as in (3, 4, 5) or (5, 12, 13).

Using the Excel technique for problems with two independent variables create a table of all possible first and second number combinations to see which of these provide integer results for the square root of the sum of their squares.

The formula for the first cell is =SQRT(B$1^2+$A2^2) which is then copied across the chosen range. Then look for cells in which this formula returns integer values. Conditional formatting helps identify the values of interest. The colour change occurs when a cell value is exactly equal to its integer part. The red type on a tan background are genuine integers, and are the result of the conditional formatting being activated. The other integers in the sheet are caused by Excel rounding the display value to 2 digits even though the held value may have many decimal places, as increasing the width of a column would reveal.

Look at the 10% Zoom View and account for the patterns you observe.