PLEASE I REALLY NEED YOUR HELP This problem is from my Probl

PLEASE! I REALLY NEED YOUR HELP! This problem is from my Problem Solving class (an advanced math class):

Solution

Lets denote 1 with letter \"a\" and -1 with \"b\", then we have the following

(a,a,a,a,a,a,a) & (b,b,b,b,b,b,b,b)

erasing 2 letter we have the following outcomes (illustration)

a,a = -aa = -(1)(1) = -1 = b

b,b = -bb = -(-1)(-1) = -1 = b

a,b = -ab = -(1)(-1) = 1 = a

Case 1: Erasing numbers within the group initially

A. (a,a, a,a, a,a, a) = (b,b, b,a) = (b,a) = a

B. (b,b, b,b, b,b, b,b) = (b,b, b,b) = (b,b) = b

thus erasing within group, we are left with one \"a\" & one \"b\", proceeding further

(a,b) = a =1 (as value of letter \"a\" is 1)

Case 2 : Erasing elements of two different group simultaneously

(a,b, a,b, a,b, a,b, a,b, a,b, a,b, b) = (a,a, a,a, a,a, a,b) = (b,b, b,a)

Erasing with in cross gruop also we are left with the the following

= (b, a) = a = 1

Therefore in whatever combination we erase the numbers we are finally left with one \"a\" & one \"b\" which eventually leads to the final value of a as illustrated above rsulting into the final value of 1.

Hence proved.....