Name: Anonymous 2006-11-12 16:24
Hay /sci/, having a little trouble with these two proofs ..
1) Let p1, p2, ... p7 be 7 points that are contained in a circle centered at (0,0) with radius 1. Prove or disprove that there are two points p(i),p(j) such that the distance between p(i) and p(j) is strictly less then 1.
Can I just say that a regular septagon with sides of length one cannot be contained within a circle of radius one? If so how would one go about in proving it?
2) Let A = {1,2,3,4,5,6,7,8,9,10,11,12,13,14}. Prove that if I select 9 distinct elements from the set A, that there are at least two pairs of elements whose sum will be exactly 15.
This is obviously true since selecting 9 will give him the majority of the numbers and since the numbers are in a sequence there will always be one number that they can pair with. But like the problem above.. how would one prove this?
1) Let p1, p2, ... p7 be 7 points that are contained in a circle centered at (0,0) with radius 1. Prove or disprove that there are two points p(i),p(j) such that the distance between p(i) and p(j) is strictly less then 1.
Can I just say that a regular septagon with sides of length one cannot be contained within a circle of radius one? If so how would one go about in proving it?
2) Let A = {1,2,3,4,5,6,7,8,9,10,11,12,13,14}. Prove that if I select 9 distinct elements from the set A, that there are at least two pairs of elements whose sum will be exactly 15.
This is obviously true since selecting 9 will give him the majority of the numbers and since the numbers are in a sequence there will always be one number that they can pair with. But like the problem above.. how would one prove this?