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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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pythagoras123Best ResponseYou've already chosen the best response.0
how did you get 26? O_O
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Gah, FFM, you just gave me another strange problem to think about. The sum of the fib numbers?
 one year ago

dumbcowBest ResponseYou've already chosen the best response.1
the answer is 57 but i don't have a mathematical proof for you i used a computer to evaluate all possible cases
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
@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?
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
Btw what is the problem source?
 one year ago

pythagoras123Best ResponseYou've already chosen the best response.0
That's why I need an explanation not just an answer
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
Competitive math probably IMO?
 one year ago

pythagoras123Best ResponseYou've already chosen the best response.0
dunno, but looks like it
 one year ago

dumbcowBest ResponseYou've already chosen the best response.1
the distribution is as follows for combinations that sum up to 6,9,12 ... 1+3+7+11+13+11+7+3+1
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
@anonymoustwo44: As this is combination 1+2+3 is same as 2+1+3
 one year ago

mykoBest ResponseYou've already chosen the best response.0
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.
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
@FoolForMath so the number 231 will be the same as the combination 321?
 one year ago

mykoBest ResponseYou've already chosen the best response.0
they bouth divisible by 3
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
so are they the same combination?
 one year ago

mykoBest ResponseYou've already chosen the best response.0
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
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
never mind me :))
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
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), 44 (3n+1 and 3n+2) 3c3 + 3c1*4c1*4c1 + 4c3 + 4c1 How about this? :D
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
3c3 + 3c1*4c1*4c1 + 4c3 + 4c3
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
did i miss something? some case?maybe
 one year ago

mykoBest ResponseYou've already chosen the best response.0
just you have to be carefull with n=0.... wait checking...
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
i only counted 3, for 3n forms {3,6,9}
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
3n+1 3n+2 for n = 0 1 and 2
 one year ago

mykoBest ResponseYou've already chosen the best response.0
never mind, you mean other thing, sry
 one year ago

shegBest ResponseYou've already chosen the best response.0
Answer for this problem is 26
 one year ago
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