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?

I first worked out that the maximum number of stones laid can be 34984, as at the end of Day 136 ther would be just 16 slaves left and the crew consists of 17 slaves.

Now, here i am assuming that the pyramid is following a pattern of: ( top - to - bottom ) 1 , 9 , 25 , 49 , 81 ... stones. Such a pyramid will have to be 29 storeys high. ( this is because, if it is any more than this it will need more stones to be laid than the number of slave-crews alive )

At the end of Day 42 there are still 260 stones to be laid, and there are2751 slaves alive. Of these 260 will be dead by the end of day 43.

So a 29 storey pyramid will have 32509 stones, which will be 87 meters high, leaving 2491 slaves alive, and would be completed in 43 days.

( If built, this would be haunted by 32509 souls who sacrificed their lives so that somebody would eventually come here after they are dead !!! ) - Ironic ???