24/7

This is a version of "The Coin Problem".

(For a discussion see here .)

Since $24$ and $7$ are relatively prime, the solution is

$24*7 - 24 - 7 = \boxed{137}$ .

By the Chicken McNugget Theorem , the answer is $24 \cdot 7 - 24 - 7 = \boxed {137}.$

We have to find THE FOBRENIUS NUMBER.........Which is equivalent to.... {[a-d][b-d]/d}-d........where gcd(a,b) is d......and ax+ by....therefore.....137!

Well I'll tell you a thing..for every $\gcd(x,y)=1$

$ax+by= \cdots many numbers...$ [ $x,y \in \mathbb{Z^+}$ (I am not sure on this) ] also not to forget $a,b \in \mathbb{non.negative} \mathbb{Z}$

the total no. of numbers which cannot be expressed in this form are

$\frac{(x-1)(y-1)}{2}$ ...now here I can't have to prove it

and the highest of them..is $\boxed{(x-1)(y-1) - 1}$ ...

now get it..