What's G and N?

Probability Level 5

Let $G$ be the answer to this problem and $N$ be the answer to this problem .

The local sports team has $N$ players and $G$ uniforms. Of course, players need uniforms; in fact, $N$ uniforms are currently being worn in today's practice. They are thus dirty, and will be sent to laundry. So the players need to pick new uniforms among the remaining $G-N$ to be used for tomorrow's practice. How many ways are there to select the $N$ uniforms to be used for tomorrow's practice? (Note that who wears which uniform doesn't matter, just whether a certain uniform is selected or not.)

The answer is 15.

1 solution

Mark Hennings
Apr 11, 2016

In these three linked problems, we are looking for the solutions of the equations $\begin{array}{rcl} 2^C + 3^C + \cdots + G^C & \equiv & N \pmod{10} \\ {G-N \choose N} & = & C \\ G & = & \tfrac16CN \end{array}$ Since $N$ must be a single digit integer, it is easy to check that the solution to these simultaneous equations is $N=4$ , $C=\boxed{15}$ and $G=10$ .

What's G and N?

The answer is 15.

1 solution

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