## 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?

A | H | |

+ | A | |

--------- | ||

H | E | E |

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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?

A | H | |

+ | A | |

--------- | ||

H | E | E |

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,

**Answer**: HEE = 100.

### References

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

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Copyright © 1996-2018 Alexander Bogomolny