Originally posted by Shiny Knight
Two sons of a farao get to build a pyramid, separately.
They both get the same amount of stones, they both get the same amount of workers.
Stones must be 1. 'cut' from the mountain, 2. 'carried' to the place of construction, 3. put in the right place. The workers at their disposal are specialised in either one of these tasks, equally divided.
...[text shortened]... I think that?
(Comments like 'now why would we care what you think?' I don't care for.)
To start, I'll make the following asumptions:
1. The time to cut each block is equal (c), and the total time to cut all the blocks is linearly dependent on the number of blocks only (n*c).
2. The time to carry each block to the site is equal (r), and the total time to carry all the blocks from the quarry to the site is linearly dependent on the number of blocks only (n*r).
3. The time to place a block depends on the height of the block's resting place only.
4. All other incidental activities (lunch, floggings, union rallys, block tipping & shuffling, etc...) don't exist, and therefore don't alter the total time! Sweeeeet...
OK, now to be able to compare the two pyramids, both need to be the same size. So the time to cut the blocks for each pyramid would be the same, and the time to carry the blocks would be the same. That leaves the placement strategy as the only possible factor in any construction time discrepancy.
Let's keep the pyramid small to start, and make it 3 levels high. And let's call the time to place a level 1 block t1, a level 2 block t2 and a level 3 block t3. The first brother would place the first 9 blocks in a 3x3 base first, followed by the 4 blocks for the 2x2 level and finally the last block on top. The total time would be:
9*t1 + 4*t2 + 1*t3
The second brother would place one block on the bottom, then 3 more blocks on the bottom to make a 2x2 base and one on the second level, then 5 more on the bottom to make a 3x3 base, plus 3 more on the seccond level, plus one on top. The total time would be:
1*t1 + (3*t1 + 1*t2) + (5*t1 + 3*t2 + 1*t3) = 9*t1 + 4*t2 + 1*t3
This is the same as the first brother, so with these assumptions the pyramids would take an equal amount of time to build.
Now, you could save some time if you had multiple teams piling up the blocks. Then, some of the second level blocks could be put up while the first layer was still being put in, overlapping the construction periods and saving some time. So in reality, the second brother's strategy might work better.