SOLUTION: A pair of dice is rolled and the product of the two numbers showing is noted. How many products are possible?

Here are all 36 ways to roll a pair of dice:

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)


Multiplying each pair we get this

  1  2  3  4  5  6
  2  4  6  8 10 12  
  3  6  9 12 15 18
  4  8 12 16 20 24
  5 10 15 20 25 30
  6 12 18 24 30 36 

The products are 

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36  

That's 18 different products.

Edwin