As promised, click here the solution.

There’s only one way to pay the stone mason after the first day of work and that’s to cut the gold bar into two pieces, a 1/7th piece and 6/7th piece.The pharaoh gives him him the 1/7th piece.

At the end of day two, the pharaoh is able to make one more cut and must pay the mason 2/7ths of the gold bar. The only way to do this is to use the larger (6/7th) piece and cut out a 2/7th piece. The pharaoh takes back the 1/7th piece and gives the 2/7th piece. Now the pharaoh has all made all of his alloted cuts and there are 3 pieces of gold bar: a 1/7th piece, a 2/7th piece, and the remaining 4/7th piece.

With these three pieces, the pharaoh is able to pay the mason every day the fraction amount of the entire gold bar that corresponds to the number of days work. I think the trickiest part was realizing that the mason can give back pieces as change.

Day 1: Pay with the 1/7th piece
Day 2: Pay with the 2/7th piece
Day 3: Pay with the 1/7th and 2/7th pieces (1/7 + 2/7 = 3/7)
Day 4: Pay with the 4/7th piece
Day 5: Pay with the 1/7th and 4/7th piece (1/7 + 4/7 = 5/7)
Day 6: Pay with the 2/7th and 4/7th pieces (2/7 + 4/7 = 6/7)
Day 7: Pay with all the pieces (1/7 + 2/7 + 4/7 = 7/7)

Of course, this is only possible if the mason doesn’t go off and spend his pay before the end of the week 🙂

I was recently given this puzzle and I thought I would share it with everyone else. So the puzzle starts…

There’s a pharaoh who wants to build a huge pyramid to compensate for his lack of self confidence. He hires a stonemason to build his pyramid in 7 days and agrees to pay the mason one gold bar upon completion for his work.

The stonemason doesn’t like the pharaoh very much nor does he trust him. So, he demands that the pharaoh pay him at the end of every day an equivalent fraction of the gold bar as the number of days that he worked. That is, after the first day of work, the pharaoh must pay him 1/7 of the gold bar, 2/7 at the end of the 2nd day, 3/7 on the 3rd, etc until the end of the 7th day where he will receive his full payment of the gold bar. The kicker is the pharaoh may only make two cuts on the gold bar. Reluctantly, the pharaoh agrees to these terms.

The question is “How does the pharaoh do it?”

As with a lot of puzzles, it helps to talk it through so feel free to post a comment or question. 🙂

I’ll post the answer later for everyone or I can answer it for myself…depending if anyone else is reading this.

Hint: There’s only one way to pay him the first day.