Page 20 - NUMINO Challenge_B1

Basic Concepts Doubly True Alphametics

Doubly True Alphametics is a math puzzle in which the letters of an
alphametic problem produce a meaningful phrase. The following example
was created by Henry Dudeney, one of the leading puzzlists of the 20th
century. This puzzle appeared in the July 1924 issue of Strand Magazine.

SEND
MORE
MONEY

Example Each letter represents a different digit. Find the digit that each
letter represents. (Note: E 5, S 9.)

SEND
MORE
MONEY

Class Notes 9 5ND
1OR 5
The leftmost digit of the sum, M, is . Since E 5 and S 9, 1 ON 5 Y
you can replace the letters of the arithmetic problem as shown on the
right. 9 5ND
1 0R5
Adding the digits in the thousands place, O can be or 1. 1 0N5Y
Since M is 1, O is .
9 5 6D
Adding the digits in the hundreds place, N cannot be 5, so it is . 1085
Adding the digits in the tens place, R cannot be 9, so it is . 1065Y

Adding the digits in the ones place, D+5 should be greater than 10.
Among the remaining digits, the only possible digit for D is .
Therefore, Y is .

17Number Puzzles