What is the maximumsize 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?
(A) 21 (B) 22 (C) 23 (D) 24 (E) 25
How do I solve it?
Can u guys show me the steps?
What is the maximumsize 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?
(A) 21 (B) 22 (C) 23 (D) 24 (E) 25
How do I solve it?
Can u guys show me the steps?
Hello paul14Welcome to Math Help Forum!
I reckon the answer is 23. Here's my reasoning.
Consider the partition of P into sets as follows:
So, for example, , etc
Then and
Now if we choose an to be in our subset , then we must not choose an , for then
Thus the subset can contain at most element from elements from , and then elements from any two of the remaining , in such a way that no two of the 's add up to .
Total:
Grandad