Question 629895
the smallest sum divisible by 9 would be 9. How many ways can we use three cards to get 9?


1 + 6 + 2 = 9 (so 162)

1 + 5 + 3 = 9 (so 153)

1 + 3 + 5 = 9 (so 135)

1 + 2 + 6 = 9 (so 126)

2 + 6 + 1 = 9 (so 261)

2 + 4 + 3 = 9 (so 243)

2 + 3 + 4 = 9 (so 234)

2 + 1 + 6 = 9 (so 216)

3 + 5 + 1 = 9 (so 351)

3 + 4 + 2 = 9 (so 342)

3 + 2 + 4 = 9 (so 324)

3 + 1 + 5 = 9 (so 315)

4 + 3 + 2 = 9 (so 432)

4 + 2 + 3 = 9 (so 423)

5 + 3 + 1 = 9 (so 531)

5 + 1 + 3 = 9 (so 513)

6 + 2 + 1 = 9 (so 621)

6 + 1 + 2 = 9 (so 612)


The next sum divisible by 9 would be 18. How many ways can we use three cards to get to 18?


7 + 6 + 5 = 18 (so 765)

7 + 5 + 6 = 18 (so 756)

6 + 7 + 5 = 18 (so 675)

6 + 5 + 7 = 18 (so 657)

5 + 7 + 6 = 18 (so 576)

5 + 6 + 7 = 18 (so 567) 


So I get a total of 24 ways