Question

I have a deck of 54 cards, and I deal all of the cards to x players, with each player getting y cards. If x is at least 2 and y is at least 5, then how many possible values of x are there?

Answer 1

4 possible values namely, (2 , 3, 6, 9 )

Explanation:

When we factorise 54 we get,

`54 = 2 * 3 * 3 * 3`

So, factors of 54 are, ( Except 1 and 54 (in pairs))

1. (2 , 27) 2. (3, 18) 3. (6 , 9)

So,

X ∈ {2, 3, 6, 9} but x ∉ { 27 , 18} since y ∉ {2 ,3}

So, there are 4 possible values for x.