# Set- i do not understand the question

1. Mar 16, 2009

### icystrike

1. The problem statement, all variables and given/known data

What is the maximum size of a subset, P, of {1, 2, 3, . . . , 50}
with the property that no pair of distinct elements of P
has a sum divisible by 7?

2. Relevant equations

3. The attempt at a solution

smallest sum = 3
largest sum = 99

factors of 7:

7 14 21 28 35 42 49 56 63 70 77 84 91 98

7 can be form by:

1 6
2 5
3 4

Last edited: Mar 16, 2009
2. Mar 16, 2009

### tiny-tim

Hi icystrike!
ok … so if 1 is in P, what can't be in P?

3. Mar 16, 2009

### icystrike

1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 !!
yes

Last edited: Mar 16, 2009
4. Mar 16, 2009

### tiny-tim

no, that's what could be in P … what can't be in P are 6 13 20 27 34 41 48, in other words everything = -1 (mod 7)

suppose 2 and 3 are also in P (as well as 1) … now what can't be in P?

5. Mar 20, 2009

### icystrike

5 12 19 26 33 40 47
4 11 18 25 32 39 46

6. Mar 20, 2009

### tiny-tim

ok, so if 1 2 and 3 are in, then all the mod6s 5s and 4s are out …

can the other mod 1s 2s and 3s be in?