Rameses wishes to build a great pyramid for his interment.

The structure will have a square base and be solidly composed of cubical stone blocks. Each level of the pyramid contains one block fewer per side as the pyramid rises.

Rameses has available an initial work force of 35,000 slaves. Each morning the available labor pool is divided into work crews of 17 slaves each. Any remainder that cannot form a full crew gets the day off but are available the following day. Each crew can lay one block of the pyramid each day.

Unfortunately, the heat of the desert sun causes the death of one member of each crew each day. Work ceases on the project when it can be determined that there will be insufficient slaves available to raise the pyramid one more level. Each stone block measures 3 meters per side.

How many days will it take to construct Rameses' pyramid? How tall will it be? How many of the original slaves survive the construction?

The number of blocks in a N levels pyramid is N(N+1)(2N+1)/6, so we need to find N so that formula isn't greater than 34984. This means 2N³/6 is approximately 34984, so N is around 47. With a calculator, 47 proves to be too high (35720 blocks would be needed), so the answer is a 46 levels pyramid, which requires 33511 blocks, thus implying 33511 deaths: 1489 slaves would survive.

Posted by e.g. on 2004-11-05 08:59:17