Bob likes 2 digit numbers n>10 such that both digits are squares. For example, 10 and 41 are two such numbers. How many of these numbers are there?

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Answer 1 · 2016-10-30T23:47:37

There are #8# numbers that fit this criteria.

Let's list the single digit numbers that are perfect squares.

There is #0, 1, 4 and 9#.

We need to pick #2# numbers out of these four numbers. Order does matter, so we use the permutation formula.

#"number of combinations" = (n!)/((n - r)!)#

#"number of combinations" = (4!)/((4 - 2)!)#

#"number of combinations" = 24/2#

#"number of combinations" = 12#

However, we cannot have #n<10#, so we have to remove #09, 01, 04, 00#, which leaves us with 8 possible numbers.