## pythagoras123 3 years ago Three different integers from 1 to 11 are selected. In how many of these combinations of 3 numbers are their sums a multiple of 3?

1. pythagoras123

how did you get 26? O_O

2. pythagoras123

erm... no.

3. inkyvoyd

Gah, FFM, you just gave me another strange problem to think about. The sum of the fib numbers?

4. dumbcow

the answer is 57 but i don't have a mathematical proof for you i used a computer to evaluate all possible cases

5. anonymoustwo44

@FoolForMath... Can I ask what combination of 3numbers is. does that mean order doesn't matter? or for instance, in this cause would 132 be same as 123?

6. FoolForMath

Btw what is the problem source?

7. pythagoras123

Homework

8. pythagoras123

That's why I need an explanation not just an answer

9. FoolForMath

Competitive math probably IMO?

10. pythagoras123

dunno, but looks like it

11. dumbcow

the distribution is as follows for combinations that sum up to 6,9,12 ... 1+3+7+11+13+11+7+3+1

12. FoolForMath

@anonymoustwo44: As this is combination 1+2+3 is same as 2+1+3

13. myko

you can try like that: the sum of numbers a,b,c is divisible by 3 if the sum of their digits is divisible by 3.

14. anonymoustwo44

@FoolForMath so the number 231 will be the same as the combination 321?

15. myko

they bouth divisible by 3

16. anonymoustwo44

so are they the same combination?

17. myko

what do you mean? the maximum sum to check in this case is: 11+10+9 = 30 (digits sum =3) you never even get to 123 or 321

18. anonymoustwo44

never mind me :))

19. Ishaan94

Every number can be expressed as 3n, 3n+1,3n+2 Case1. 3n,3n,3n Case2. 3n, 3n+1,3n+2 Case3. 3n+2,3n+2,3n+2 Case 4. 3n+1,3n+1,3n+1 In the set {1,2,..,11} 3 (3n forms), 4-4 (3n+1 and 3n+2) 3c3 + 3c1*4c1*4c1 + 4c3 + 4c1 How about this? :D

20. Ishaan94

3c3 + 3c1*4c1*4c1 + 4c3 + 4c3

21. Ishaan94

did i miss something? some case?maybe

22. Ishaan94

myko?

23. myko

just you have to be carefull with n=0.... wait checking...

24. Ishaan94

i only counted 3, for 3n forms {3,6,9}

25. Ishaan94

3n+1 3n+2 for n = 0 1 and 2

26. myko

never mind, you mean other thing, sry

27. myko

you right, good job

28. sheg

Ishaan is correct

29. sheg

Answer for this problem is 26

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