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 |