Question

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?

Answer 1

how did you get 26? O_O

Answer 2

erm... no.

Answer 3

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

Answer 4

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

Answer 5

@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?

Answer 6

Btw what is the problem source?

Answer 7

Homework

Answer 8

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

Answer 9

Competitive math probably IMO?

Answer 10

dunno, but looks like it

Answer 11

the distribution is as follows for combinations that sum up to 6,9,12 ...

1+3+7+11+13+11+7+3+1

Answer 12

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

Answer 13

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.

Answer 14

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

Answer 15

they bouth divisible by 3

Answer 16

so are they the same combination?

Answer 17

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

Answer 18

never mind me :))

Answer 19

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

Answer 20

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

Answer 21

did i miss something? some case?maybe

Answer 22

myko?

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

never mind, you mean other thing, sry

Answer 27

you right, good job

Answer 28

Ishaan is correct

Answer 29

Answer for this problem is 26