October 2022 - Math Problem

This Month’s Problem

Consider this list of numbers 

 1, 1, 1, 4, 4, 4, 7, 7, 7, 10, 10, 10

Pick any 3 numbers from the list and add them together.  

Repeat the process with a new set of numbers from the original list.  

What do you notice about the sums? 

Solution

The sum is always a multiple of 3.  

Can you increase the list by six numbers so that selecting three of them will always result in a sum that is a multiple of 3?

Department