# The trouble in building a pyramid

Shiny Knight
Posers and Puzzles 21 Jun '05 20:17
1. 21 Jun '05 20:171 edit
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.

In Dutch: 1.houwers, 2.sjouwers en 3.bouwers. π

Son A is a conservative guy. He builds like this:
First the base.
-----

Then the next level
---
-----

etcetera
-
---
-----

Son B decides to build pyramid by pyramid. Radical.

After
---

he doesn't go
----

but
-
---

All in 3 dimensions ofcourse. (The spaces disappear when posted, by the way.)

Which son would finish first?

This is not a riddle. More of a thought-experiment. I have a theory, but I'm curious first what y'all make of this.

If I'm 'right', it could rock the world of egyptology!
π²

Maybe there's a good riddle (bonus): now why would I think that?π

(Comments like 'now why would we care what you think?' I don't care for.)
2. PBE6
Bananarama
21 Jun '05 21:19
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?π

(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.
3. 21 Jun '05 21:54
Originally posted by PBE6
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 ...[text shortened]... periods and saving some time. So in reality, the second brother's strategy might work better.

I reckoned about the same: the stone-demand on buildingsite B would be more constant.

But I'm open for other opinions ofcourse.
4. sonhouse
Fast and Curious
22 Jun '05 15:26
Originally posted by Shiny Knight

I reckoned about the same: the stone-demand on buildingsite B would be more constant.

But I'm open for other opinions ofcourse.
what if you started with one block in the center, built it up with 4
blocks on top of that, each halfway sticking out and then the next one
like 6 blocks and so forth, building it upside down then simply
turning it over at the end. Any faster?
5. 22 Jun '05 19:54
Originally posted by sonhouse
what if you started with one block in the center, built it up with 4
blocks on top of that, each halfway sticking out and then the next one
like 6 blocks and so forth, building it upside down then simply
turning it over at the end. Any faster?
Yes, alright, the farao had a 3rd son, all grown up. The wise farao only gave him some blocks to play with. Now why would that be?
6. sonhouse
Fast and Curious
22 Jun '05 22:40
Originally posted by Shiny Knight
Yes, alright, the farao had a 3rd son, all grown up. The wise farao only gave him some blocks to play with. Now why would that be?
course he was very strong, able to lift those blocks by himself....
7. 23 Jun '05 07:02
Originally posted by sonhouse
course he was very strong, able to lift those blocks by himself....
Still, the third pyramid is much smaller than the other two.
Now why would...
8. 23 Jun '05 22:441 edit
The first guys strategy is better. Tp get stones to the top of the pyramid you push them up a ramps that are supporetd by the existing stones. If you build the pyramid layer by layer you can either have a single straight ramp up one face, so you get all your stones to the top, or your ramp can spin round the faces of the pyramid in a corkscrew.

If you build pyramid by pyramid you have to somehow get the stones off at all levels so you need a lot more ramps, and they can't spin around the faces so they are great long things.
9. 23 Jun '05 23:291 edit
Originally posted by iamatiger
The first guys strategy is better. Tp get stones to the top of the pyramid you push them up a ramps that are supporetd by the existing stones. If you build the pyramid layer by layer you can either have a single straight ramp up one face, ...[text shortened]... d they can't spin around the faces so they are great long things.
I assumed they used wooden levers to get those stones up. But I guess that's a riddle in itself how they did that in reality, especially those extra heavy ones at the top.
10. sonhouse
Fast and Curious
24 Jun '05 11:29
Originally posted by Shiny Knight
I assumed they used wooden levers to get those stones up. But I guess that's a riddle in itself how they did that in reality, especially those extra heavy ones at the top.
well that one was easy, they used helium balloons.
11. 24 Jun '05 13:34
Originally posted by sonhouse
well that one was easy, they used helium balloons.
Must have been one happy building site. Imagine the sound:

π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅
"Joho, joho, it's off to work we go..."
12. sonhouse
Fast and Curious
27 Jun '05 03:41
Originally posted by Shiny Knight
Must have been one happy building site. Imagine the sound:

π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅ π΅
"Joho, joho, it's off to work we go..."
How bout the theory floating around, ehem, that said:
Since it is well known that early man (not sure how "early" that would
be considering there is a lot more early than Egypt)
could not have possibly been smart enough to have pulled off the
construction of the Pyramids, they obviously had help from
friendly aliens.
This is somehow supposed to be taken seriously. I can for sure
imagine aliens landing 4000 years ago and see the poor egyptian
slobs struggling to get some obilisk up in the air and showed
pity on the struggling humans and used their antigravity beam
to pop the thing in place, and everyone thought that was great
so the aliens, pumped up by now on all the adulation, said
You think THAT was something, We'll show you something.....
13. 27 Jun '05 07:22
Originally posted by sonhouse
How bout the theory floating around, ehem, that said:
Since it is well known that early man (not sure how "early" that would
be considering there is a lot more early than Egypt)
could not have possibly been smart enough to have pulled off the
construction of the Pyramids, they obviously had help from
friendly aliens.
This is somehow supposed to be ...[text shortened]... by now on all the adulation, said
You think THAT was something, We'll show you something.....
I like the idea of aliens checking in every 3000 years or so; next time they come around they are in for quite a shock. (They probably get blasted out of the sky by the U.S.)

Aliens could be the answer to why Egyptians lost the ability of building a pyramid like the one at Giza. After the first they build one again, equally beautiful. And they build a third, supposedly offset 17 degrees so it matches Orion's belt. (Beauvals theory.)

But the south-east corners of these three pyramids are 'exactly' aligned (pretty much so).

So here's the new theory: they used (with or without alien help) 'pyramid by pyramid'-building (starting at the SE corner) and never finished the third.

Maybe if we it complete it, they will come.π
14. 27 Jun '05 19:29
Originally posted by Shiny Knight
I assumed they used wooden levers to get those stones up. But I guess that's a riddle in itself how they did that in reality, especially those extra heavy ones at the top.
The raps theory is pretty much accepted, but archaeologists can't decide whether the ramps were spiral (uses less ramp stuff, but has tricky corners) or straight.

Either way the ramps have to be a lot shallower in slope than the side of the pyramid, to support themselves.
15. sonhouse
Fast and Curious
11 Jul '05 20:19
Originally posted by iamatiger
The raps theory is pretty much accepted, but archaeologists can't decide whether the ramps were spiral (uses less ramp stuff, but has tricky corners) or straight.

Either way the ramps have to be a lot shallower in slope than the side of the pyramid, to support themselves.
My guess is they knew full well a spiral ramp was causing a lot of
extra work, redoing the logs every couple of feet. Unless,,unless(big
mental flash hereπ: They used slightly conical rolling logs that would
match the spiral curve as they roll it up. That could be a serious
alternative to the straight ramp idea, which seems to me to be
perfectly reasonalbe too. Come to the latest 90 degree bend, just
take out the logs and put them in from the 90 degree away side
and continue on, much less log manipulation than taking regular
logs up a spiral, unless they figured out a conical shaped log.
It wouldn't take a whole lot of conicalness to do the job since you
have a huge spiral, maybe tapered down one inch less than the
other end. The tricky part would be to do the taper smoothly and
reproducably for hundreds of logs.