Alan and Bob are trying to figure out two numbers. They know that both numbers are integers between 1 and 100 (but not 1 or 100). Alan knows the product of the numbers, and Bob knows the sum. Their conversation goes as follows:
Alan: I can't tell what the two numbers are.
Bob: I knew you couldn't.
Alan: Ok, now I know the numbers.
Bob: Now I know them, too.
What are the two numbers?
n() = set order, | = set intersection, -> = is contained in set
x != 1, y != 1
Statements are 1-4
alan = alans number, bob = bobs number.
Define S as the set generated from x+y such
that (x,y) are non-unique factors of x*y.
1,2: bob->S
Define S(m) as the set generated by x+y
such that x*y=m
3: n(S(alan) | S) = 1
Define M(s) as the set generated by x*y
such that x+y=s.
Define U(M) as the set of m->M
such that n(S(m) | S) = 1
4: n(U(M(bob))) = 1
To solve, first obtain S. Then obtain
n(U(M(s))) for s->S
you find n(U(M(11))) >= 2, but n(U(M(17))) = 1
with n(S(52) | S) = 1.
this is a solution only if exhausted
for all s->S such that s >= 98+99.
attempt..
