Interview riddle On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview :
$$3\times 4=8$$ 
$$4\times 5=50$$ 
$$5\times 6=30$$ 
$$6\times 7=49$$ 
$$7\times 8=?$$
We have not managed to solve it so far, all we know is the solution (which was given after we had given up) :

 $224$

How do we find this solution ?

Easy, just define 
$$\begin{array}{rcl}a \times b &=& 
\hspace{10.5pt}(a-4)(b-5)(a-5)(b-6)(a-6)(b-7)(a-7)(b-8)/72 + \\&& 25(a-3)(b-4)(a-5)(b-6)(a-6)(b-7)(a-7)(b-8)/18 + \\&& 15(a-3)(b-4)(a-4)(b-5)(a-6)(b-7)(a-7)(b-8)/8 \hspace{5.25pt}+ \\&& 49(a-3)(b-4)(a-4)(b-5)(a-5)(b-6)(a-7)(b-8)/36 + \\&&\hspace{5.5pt}7(a-3)(b-4)(a-4)(b-5)(a-5)(b-6)(a-6)(b-7)/18\end{array}$$
