Pick any 3 numbers from the following list, circle them, and find their sum
1 , 1 , 1 , 4 ,4 , 4, 7 , 7 , 7, 10, 10 ,10
Repeat the process with a new set of numbers from the original list.
What do you notice about the sums?
Can you explain why this happens?
Answer:
The sum is always a multiple of 3.
This happens because each of the numbers is one more than a multiple of 3 (1 = 0 + 1, 4 = 3 + 1, 7 = 6 + 1, 10 = 9 + 1). When you add any three of them, you are adding three multiples of 3 plus three 1s, which will always result in a multiple of 3.
Are there other numbers you can add to the list so that selecting three of them will always result in a sum that is a multiple of 3?
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