Sure, let's solve the problem step by step.
1. Understanding the Problem:
- Paul rolled a number cube 4 times, and each roll resulted in a different number.
- The product of the four numbers is 60.
- The sum of the four numbers is 13.
- Each roll had to result in a number between 1 to 6 (since it's a standard number cube).
2. Listing Possible Numbers:
We need to pick 4 different numbers from {1, 2, 3, 4, 5, 6}.
3. Finding Combinations:
We need to find which combination of 4 different numbers among the possible numbers will satisfy both conditions:
- Their product is 60.
- Their sum is 13.
4. Checking Each Combination:
We can test the combinations step-by-step:
- Let's test if the numbers 1, 2, 3, and 4 work:
- The sum is 1 + 2 + 3 + 4 = 10 (not 13, so this combination doesn’t work).
- The product is 1 2 3 4 = 24 (not 60, so this combination doesn’t work).
- Let's test the numbers 1, 2, 4, and 6:
- The sum is 1 + 2 + 4 + 6 = 13 (checks for the sum condition but let's check the product condition).
- The product is 1 2 4 6 = 48 (not 60, so this combination doesn’t work).
- Let's test the numbers 1, 3, 4, and 5:
- The sum is 1 + 3 + 4 + 5 = 13 (checks for the sum condition).
- The product is 1 3 4 * 5 = 60 (also checks for the product condition).
This combination meets both conditions. Therefore, the numbers Paul rolled are:
1, 3, 4, and 5.
So, Paul rolled the numbers 1, 3, 4, and 5.
