1997 PMWC Problems/Problem I12

Problem

In a die, 1 and 6, 2 and 5, 3 and 4 appear on opposite faces. When 2 dice are thrown, product of numbers appearing on the top and bottom faces of the 2 dice are formed as follows:

• number on top face of 1st die x number on top face of 2nd die
• number on top face of 1st die x number on bottom face of 2nd die
• number on bottom face of 1st die x number on top face of 2nd die
• number on bottom face of 1st die x number on bottom face of 2nd die

What is the sum of these 4 products ?

Solution

Let be the two numbers at the top of the two dice. Then