Henry Ernest Dudeney/Puzzles and Curious Problems/104 - Letter-Figure Puzzle/Solution

by : $104$

 * Letter-Figure Puzzle
 * A correspondent (C. E. B.) sends the following.
 * It is not difficult, if properly attacked:


 * Every letter represents a different digit, and, of course, $A C$, $B C$ etc., are two-figure numbers.


 * Can you find the values in figures of all the letters?

Solution
A B C D E F H J K L - 1 3 5 7 8 9 6 4 2 0

Solution
Trivially from $(8)$ and $(9)$
 * $L = 0$

Hence immediately from $(1)$:
 * $A = 1$

Hence:
 * $10 < A C < 20$

From $(2)$ we inspect pairs ending in the same digit whose divisor is that same digit twice, and this leads us to:
 * $C = 5$

Hence: