BrainDen.com - Brain Teasers

# HoustonHokie

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## Everything posted by HoustonHokie

1. Bonanova's signature keeps taunting me regarding this puzzle, so I had to do some research to see if I could understand some of the basics.
2. I see some of it now:
3. Clarification request: 1. Does passing a roll over a plate that already has two rolls count as passing over 1 or 2 rolls? 1a. If consecutive plates have 1, 1, & 2 rolls respectively, can a roll be picked up from the first plate and moved beyond the plate with 2 rolls? 2. Does the waiter have to set the roll down on the next plate following the plate with the second roll, or can he keep moving with the roll, provided he does not pass over a third roll? In other words, if you pass over two rolls and the next plate is empty, does the waiter have to set the roll down on the empty plate, or can he move it to a plate that's not empty?
4. Here's how I think about it:
5. Unless I'm mistaken, the trick is in
6. ## Plates that cover a table

I'm going to put aside the hexagonal packing stuff for a while and try to tackle these proofs. At HoustonHokie's Hexagonal Hamburgers and Hash, deep in the Heart of Texas, all the tables are hexagons (except for the big circular table in the middle), and the answer might be, well, a little bit different.
7. ## Plates that cover a table

Yes we do, because we need to make sure that the coverage is the most effecient possible.
8. ## Plates that cover a table

No, but it is inferred.
9. Here's my proof:
10. ## Plates that cover a table

Perhaps this will help illustrate what we've been saying (I always like a good drawing ).
11. Like you, I have a long proof, but I got the same answer. Then I drew it out (as well as the other two solutions that have been posted), and confirmed we're right. I'm looking for that "magic bullet" answer - there always seems to be one

13. ## Plates that cover a table

A quick check reveals that
14. ## Plates that cover a table

Or I could make it a little better...
15. ## Plates that cover a table

Combining this table size with PT's optimal coverage arrangement, I get:
16. ## Plates that cover a table

With that in mind, it looks like the biggest table would be
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