Areteem: MCIII Number Theory 2.19

Online Course Discussion Forum

Hello,

I don't really know how to do this problem, I tried to find a way to pair it:

1 97 98

2 94 96

3 92 95

4 89 93

but its not really following any pattern, and I don't really know how to pair (or group) it.

Also, if I don't find a way, I won't be sure if it is because I haven't found it, or there really isn't one.

Thank you!

Tina Jin

Hint: parity.

Thank you! Here's what i did:

let a_i=student that is equal to the other students in the row's sum

then a1+a2+...+an=98*99/2-(a1+a2+...+an)

moving the a1+a2+...+an to the other side and dividing by two yeilds

a1+a2+...+an=98*99/4≠integer, so contradiction and hence not possible.

Thanks,

Tina Jin