Answer to October 5, 1998 Problem

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 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