Question

Tim had nine cards, each with a different number from 1 to 9 on it.

He put the cards into three piles so that the total in each pile was 15.
How could he have done this?

Can you find all the different ways Tim could have done this?

All.​

Answer 1

Tim had nine cards with each having a distinct number from 1-9, meaning no number should be repeated twice while he tried to arrange them in piles while each pile should have a total of 15 when these numbers in the card are added all together.

I would arrange the ways below in rows and columns to make it easier to understand:

Ways Ist Pile 2nd Pile 3rd Pile

1st way: 5, 1, 9 2, 4, 6, 3 7, 8

2nd way: 1, 6, 8 5, 7, 3 4, 2, 9

3rd way: 9, 2, 3 , 1 4, 5, 6 8, 7

4th way: 4, 9, 2 7, 8 6, 3, 5, 1

5th way: 8, 2, 4, 1 9, 6 7, 5, 3

6th way: 1, 2. 3, 4, 5 7, 8 9, 6

7th way: 3, 8, 4 4, 6, 5 9, 1, 5

8th way: 1, 2, 5, 7 3, 4, 8 6, 9

9th way: 8, 5, 2 9, 6 1, 3, 4, 7