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?

Back in the pyramid building days, they didn’t have spreadsheets or fancypants calculators. I’m wondering about how they would logistically build this to "spec"?

What I mean is, would they be able to do all the calculations to figure out that the bottom level would be 46 blocks on a side? In that case they would just start laying the blocks for the bottom layer, and start building up from there, and stop when they placed the top block. Near the end they would be able to tell how many blocks were left to place, so they would form the correct number of crews the last day.

Or would they not be able to calculate the size of the bottom level ahead of time? In that case maybe they do this: They place one block. Then they place 3 blocks to make the bottom layer 2x2, and place another block on top to make a mini pyramid. Then they place 5 on the bottom layer, 3 on the next layer, and place the top block on, again making a larger, though still mini, pyramid. Following in this fashion, after completing a mini pyramid, the would increase the size of the bottom layer by one on a side, and fill up the rest of the layers to make another mini pyramid. Once the pyramid starts to get larger, and their slave resources get smaller, they would be able to pause at the end of each mini pyramid and say "the base of our current pyramid is n on a side. This means we will need to add (n+1)^2 blocks to get to the next mini pyramid. Do we have enough men to do that?"

Just trying to think how they would actually go about doing this. Wondering if anyone else was thinking along the same lines. Perhaps not, but I thought I’d take a shot and see =)