In how many ways can 81 be written as the sum of three positive perfect squares if the order of the three perfect squares does not matter?

We are being asked to determine how many ways can 81 be written as the sum of three positive perfect squares. It should be also highlighted that the order of the three perfect squares is not important.

We have the first combination below:

81 = 9² + 0² + 0²

The next combination is below:

81 = 8² + 4² + 1²

The next combination is below:

81 = 7² + 4² + 4²

The next combination is below:

81 = 6² + 6² + 3²

The answer is 4. There were four possible combinations.