A typical die has numbers 1 to 6 arranged on its sides so that the sum of each pair of numbers on opposite side is equal. What is the greatest product of two numbers on opposite sides?

A typical die has numbers from 1 to 6 arranged such that the sum of the numbers on opposite sides is always equal to 7. This gives the following pairs of opposite sides:

- 1 and 6
- 2 and 5
- 3 and 4

To find the greatest product of two numbers on opposite sides, let's calculate the products of each pair:

- \( 1 \times 6 = 6 \)
- \( 2 \times 5 = 10 \)
- \( 3 \times 4 = 12 \)

The greatest product is \( 3 \times 4 = 12 \).

So, the greatest product of two numbers on opposite sides of the die is **12**.

Do you want further details or have any other questions?

Here are 5 related questions:
1. What is the smallest product of two numbers on opposite sides?
2. How many different ways can you arrange numbers on a die while keeping the same rule for opposite sides?
3. If a die has numbers 1 to 8, how would you arrange them to follow a similar rule for opposite sides?
4. What is the average of the products of all the opposite sides?
5. How can you verify that a die follows the sum of 7 rule?

**Tip:** In many games, knowing the opposite faces on a die can be useful for quick mental calculations!

Discover how to find the greatest product of two numbers on opposite sides of a die where the sum of each pair of opposite sides equals 7. This solution involves calculating products of numbers 1 to 6 and is ideal for students in Grades 4-6.

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