October 5, 1998
Problem of the Month

Unit Fraction Problem

Find seven different unit fractions whose sum is 1. In other words, determine the values for a, b, c, d, e, f, and g in the following equation:

1   1   1   1   1   1   1
- + - + - + - + - + - + - = 1
a   b   c   d   e   f   g
  

where a, b, c, d, e, f, and g are all different positive integers.

Solution to the Problem:

1   1   1    1    1    1    1
- + - + - + -- + -- + -- + -- = 1
2   6   8   12   20   24   30

or 


1   1   1   1    1    1    1
- + - + - + - + -- + -- + -- = 1
3   5   6   8   10   20   40        

or

1   1   1    1    1    1    1
- + - + - + -- + -- + -- + -- = 1
2   4   8   16   36   48   72

or

1   1   1    1    1    1    1
- + - + - + -- + -- + -- + --- = 1
2   4   8   16   32   34   544

or 

1   1   1   1    1    1    1
- + - + - + - + -- + -- + --- = 1
3   4   6   9   13   18   156       

or 

1   1   1   1    1    1    1
- + - + - + - + -- + -- + -- = 1
3   5   6   9   12   18   20        

or 

1   1   1   1    1    1    1
- + - + - + - + -- + -- + -- = 1
3   4   7   8   14   24   28        

     

Correctly solved by:

1. Trey Genda	Winchester, VA
2. Kaveh Sadeghzadeh	Williamsburg, VA
3. Ginger Anderson	Winchester, VA
4. Barrett Waybright	Winchester, VA
5. Michael Leatherman	Norfolk, VA
6. Anna Hauger	Winchester, VA
7. Jason Aikens	Winchester, VA
8. Mike Biggs	Charlottesville, VA
9. Andrew Crosby	Winchester, VA

Send any comments or questions to: David Pleacher