[math puzzle] Payment in fraction of gold bars.

[pier4r]

You are a generous employer. You pay one of your employee with one gold bar each week.

The point is that you pay him with 1/7 of the gold bar each day of the week.

The gold bar is a prism with trapezoid base or, simplified, with a rectangular base. What is the minimum amount of cuts that one need to do to be able to pay the employee?

A guy in the MathJam meeting today was able to find a really "out of the box" but valid solution (in payments terms, with the employee cooperation) with only 2 cuts. Really neat.

Also this problem for me could be linked to the egyptian fraction problems.

[SlideRule]

Cut the bar into 3 unequal pieces as follows:
piece 1; 1/7 of the total bar from the left end = P1
piece 2: 2/7 of the total bar from the right end = P2
piece 3; 4/7 of the remaining bar = P4
Day 1 = +P1
Day 2 = -P1+P2
Day 3 = +P1+P2
Day 4 = -P1-P2+P4
Day 5 = +P1+P4
Day 6 = -P1+P2+P4
Day 7 = +P1+P2+P4

If you ignore the P, the +#'s add to the desired daily amount
ps: (+) mean give to employee & (-) means take from employee

BEST!
SlideRule