Astable roommate problem with 4 students a, b, c, d is de ned as follows. each student ranks the other three in strict order of preference. a matching is de ned as the separation of the students into two disjoint pairs. a matching is stable if no two separated students prefer each other to their current roommates. does a stable matching always exist? if yes, give a proof. otherwise give an example roommate preference where no stable matching exists.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right