# 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?

Oct 30, 2016

There are $8$ numbers that fit this criteria.

#### Explanation:

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

There is $0 , 1 , 4 \mathmr{and} 9$.

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)!)

$\text{number of combinations} = \frac{24}{2}$

$\text{number of combinations} = 12$

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