Question

Ivan also decides to try putting together the “Multiples of 3” set from the numbers sitting around. How can he know if a number is a multiple of 3? (Hint: Build a lot of different multiples of 3. Then look at the sum of the digits of each number.

Answer 1

Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ...

The two digit numbers in that list above all have their digits adding to some other multiple of 3

• 1+2 = 3
• 1+5 = 6
• 1+8 = 9
• 2+1 = 3
• 2+4 = 6
• 2+7 = 9
• 3+0 = 3
• 3+3 = 6
• 3+6 = 9

and so on.

Therefore, the rule is: If the digits add to a multiple of 3, then the original number is a multiple of 3.