Outline Mathematics
Number Theory

A Cryptarithm: A + HA = HEE

In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?

 AH
+ A
---------
HEE

Solution


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Copyright © 1996-2018 Alexander Bogomolny

Solution

In the addition problem below, different letters stand for different digits. AH represents a two-digit number and HEE represents a three-digit number. What number does HEE represent?

 AH
+ A
---------
HEE

The leftmost digit of HEE is obtained from adding a one-digit carry to a one-digit A,A,H,E. It may only be 1,0,1,2,3,9,. Therefore, H = 1,H = 0,A = 0,E = 0,H = 1,A = 1,E = 1. But in order to get a carry from the tens column to the hundreds column in the first place, A has to be 9,0,1,2,3,9. It then follows that E = 0,0,1,2,3,9.

Answer: HEE = 100.

References

  1. G. Lenchner, Math Olympiad Contest Problems For Elementary and Middle Schools, Glenwood Publications, NY, 1997

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