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        riddles >> medium >> Tutankhamun's Pyramid of Giant Bowling Balls
        
(Message started by: Quetzycoatl on Dec 29^th, 2003, 12:23pm)

Title: Tutankhamun's Pyramid of Giant Bowling Balls
Post by Quetzycoatl on Dec 29^th, 2003, 12:23pm

This is exactly the same puzzle as Tutankhamun's Pyramid posted by THUDandBLUNDER, except this time King Tut decides he wants to make a triangular pyramid out of enourmous bowling balls.

Tutankhamun wishes to build a Great Pyramid for his after-life. It must be solidly composed of giant bowling balls and its base must be triangular. Tutankhamun has available an initial workforce of 35,001 slaves. Each morning the available labour pool is divided into workgroups of 17 slaves each. Any remaining slaves that cannot form a full workgroup get the day off, but are available for work the following day. Each workgroup can roll one ball into place each day. However, the merciless desert heat causes the death of one member of each workgroup per day. Work stops on the Pyramid when it can be shown that there will not be sufficient slaves available to raise the Pyramid another level.

1) How many levels will it have?

2) How many of the original slaves will survive its construction?

3) How many days will it take to construct the Great Pyramid?

Title: Re: Tutankhamun's Pyramid of Giant Bowling Balls
Post by towr on Dec 29^th, 2003, 2:47pm

::[hide]
1&3) 59 levels, 1011 slaves survive
[/hide]::

Title: Re: Tutankhamun's Pyramid of Giant Bowling Balls
Post by Quetzycoatl on Dec 29^th, 2003, 2:57pm

Hmm, thats close to what I got but not quite.

I get:
[hide]
1) 58 levels (34220 balls)
2) 909
3) 63 days
[/hide]

Title: Re: Tutankhamun's Pyramid of Giant Bowling Balls
Post by towr on Dec 29^th, 2003, 3:04pm

oops, I'd accidentally added 2000 illegal immigrants to the work force..

Try making a pyramid like structure one a hexagonal base, this should proof more interesting. And provide a few more problems to overcome.

Title: Re: Tutankhamun's Pyramid of Giant Bowling Balls
Post by Quetzycoatl on Dec 31^st, 2003, 1:31pm

It's hard to get a nice hexagon using square bricks or balls. Plus the top level either needs to be rather flat (ie composed of multiple bricks/balls) or it can't be a hexagonal.

Title: Re: Tutankhamun's Pyramid of Giant Bowling Balls
Post by towr on Jan 1^st, 2004, 5:10am

One ball can be said to be hexagonal, at least just as much as one ball is triangular.. and of course 7, 19, etc balls form perfectly nice regular hexagons.
The problem of course not the base layer, but those on top of it.. But you'll get a pretty nice hexagonal pyramid if you just do your best to cover every layer from the ground up.. Besides, even though they may not be all regular, the other layers will still be hexagonal. And that's exactly what makes it interesting imo..