Archive > The Amazing Race 16 Spoilers/Speculation

TAR16 - EP6: "Cathy Drone?" (France)

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chill_sd:

--- Quote from: apskip on March 22, 2010, 09:23:26 PM ---OK, it's time to reveal in two parts what I know about the Champagne Pyramid Trick.

First you have to have a stable formation, a tetrahedron or triangular pyramid  that will use up 680 wine glasses. This is a lot harder than it sounds. I did a little by trial and error:
1. I looked at an extended bowling pin arrangement and discovered that with 15 glasses in the bottom triangle the total in the stack of having one less in each ascending row would be 666. Unless a square pattern fits better (which as you will see in #2 is not the case)you have to add glasses into the formation somewhere, which is one for each level except the top one (which has to be just 1)
--- End quote ---

This is not accurate.  A tetrahedral stack with a base of 15 has the following number of glasses, starting at the top:

1+3+6+10+15+21+28+36+45+55+66+78+91+105+120 = 680 exactly.

apskip:
chill_sd,
You are correct. When I did that addition (by hand) I somehow left off 45 (9th level going up) from the cumulative addition of that sequence due to having the 9 in my first column but not putting anything across from it in the second column and not being able to find that mistake. That explains why I could not make it add up exactly. Thanks for getting it right.

Cocoa:
I calculated and wondered how to stack 680 glasses in 15 levels while in the hospital, and I cannot seriously get it! Kudos chill!

Dånooky:

--- Quote from: uycocoa on March 25, 2010, 06:54:56 PM ---I calculated and wondered how to stack 680 glasses in 15 levels while in the hospital, and I cannot seriously get it! Kudos chill!

--- End quote ---
Try this:
In a triangular fashion
1st level: 1
2nd level: 1 + 2
3rd: 1 + 2 + 3
...
15th: 1 + 2+ 3 + ... + 13 + 14 + 15

If you sum all levels you get (levels * glasses):
15*1 + 14*2 + 13*3 + ... + 9*7 + 8*8 + 7*9 + ... + 3*13 + 2*14 + 1*15
Which equals
2*[15*1 + 14*2 + 13*3 + ... + 9*7] + 8*8 = 680

mswood:
Since I was so hard at Louie & Michael and ragging on them for winning a leg, when only Joe & Heidi actually took longer to perform that leg.

With times we can now say that Louie & Michael did in fact run the fastest leg (in fact the only time they have, even with 3 wins, go figure).

They finished the leg 1 minute faster then Carol & Brandy, and with the trouble they had in getting the first half of the leg done, I think they need to give a big thanks to the the lady giving them not only the correct directions (which Carol & Brandy were the only other team to get), but having someone drive them there.  I am willing to guess that was the deciding factor in their winning the leg, not just their performance.

Can I reiterate how much I hate it when teams get someone to lead them the whole way.  Directions I don't mind (as everyone does this), but drive yourself for christ sake.

Oh and Dan & Jordan while it was great that you guys manage to complete the detour.  Boy's it was the single dumbest thing you have done on this race, as that cost you roughly an additional 2 and a half hours over the team that got to the site after you did.  Its the first time they have been the team to actually take the most time to complete the day's task (I would guess that even Jordan & Jeff finished the leg faster).

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