Problem of the Week 12

Find seven different unit fractions whose sum is 1.

1/a + 1/b + 1/c + 1/d + 1/e + 1/f + 1/g = 1.

 

Alternate Problem 12

Using the numbers 2/7, 4/7, 6/7, 8/7, 10/7, 12/7, 14/7, 16/7, and 18/7 only once, place them in the circles such that the sum on each side is 34/7.

 week12

Extension Problem 12

The following sequence of relations has a pattern:

(2 x 13 + 4 x 7)/2 = 27
(4 x 31 + 6 x 21)/2 = 125(6 x 57 + 8 x 43)/2 = 343
(8 x 91 + 10 x 73)/2 = 729
(10 x 133 + 12 x 111)/2 = 1331

Develop a similar sequence of relations, but use 3, 5, 7, and 9 as the first quantity inside the parenthesis.