What's C and N?

Geometry Level 5

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

Let $WXYZ$ be a nondegenerate rectangle such that $WX = C$ and $XY = N$ . Let $P, Q$ be the midpoints of $WX, XY$ respectively. Suppose $WY$ and $ZP$ intersects on $R$ , and $WY$ and $ZQ$ intersects on $S$ . What is the area of the triangle $RSZ$ ?

The answer is 10.

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 $N=4$ , $C=15$ and $G=\boxed{10}$ .

What's C and N?

The answer is 10.

1 solution

0 pending reports