Cryptarithms

From Diane Resek, Professor Emerita of Math, SF State
These problems came from Some Problems Stolen from Various Places, by Don Colman.

In the following addition problem, the letters A, B, and C stand for three different digits. Figure out which digit each letter stands for and explain why your answer is the only possible one.

	A	A
+	B	B

C	B	C

Now, just as in true life, the following calculation is not only hard, but it is in fact impossible. Explain why this subtraction problem cannot be performed with each letter standing for a different digit.

S	P	E	N	D
-	L	E	S	S

M	O	N	E	Y

This puzzle is a variation Henry Ernest Dudeney.s equation, which was published in the July 1924 issue of Strand Magazine:

	S	E	N	D
+	M	O	R	E

M	O	N	E	Y

According to the website www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/:

Cryptarithms are puzzles in which letters or symbols are substituted for the digits in an arithmetical calculation. Algebraic expressions might be regarded as cryptarithms of a sort, but algebra is not generally considered to be mathematically recreational. Cryptarithms have existed for centuries, and it is doubtful if it will ever be known when such puzzles were first devised. If a cryptarithm utilizes letters in place of the digits, and these letters form sensible words or phrases, the puzzle is termed an alphametic. J. A. H. Hunter coined the term in 1955.

You can find more cryptarithms on the website www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/ and in the book Getting Smarter Every Day (Books D, E, and F) by Dale Seymour.