Henry Ernest Dudeney/Modern Puzzles/72 - Alphabetical Sums/Solution

by : $72$

 * Alphabetical Sums

Solution
565  -- 35)19775    175    ---     227     210     ---      175      175      ---

Proof
We have immediately that $R \times R = R \pmod {10}$.

However, because $R \times PR = MTV$ it is clear $R \ne 1$ and (obviously) $R \ne 0$.

So $R = 5$ or $R = 6$.

To get $V$ in the fifth line it is clear $D = 0$.

We have that $K = 2 M$ and so:
 * if $R = 5$ then $M \in \set {1, 2, 3, 4}$
 * if $R = 6$ then $M \in \set {1, 2, 3, 4, 5}$.

If $R = 5$ then $S$ must be even in order for $D$ to be $0$.

If $R = 6$ then $S = 5$.

The rest of the puzzle falls to trial and error.