Archive > The Amazing Race 16 Spoilers/Speculation
TAR16 - EP6: "Cathy Drone?" (France)
Hooky:
--- Quote from: chill_sd on March 22, 2010, 04:10:42 PM ---PS - I would have used a similar trick to add up the numbers on a clock face (I don't remember which season, but it was part of a task involving finding numbers to open a safe). The clock has 12 numbers, which can be paired up 1-12, 2-11, 3-10, 4-9. 5-8 and 6-7. Six pairs that add up to 13. 6 times 13 = 78, which is the sum of the numbers 1 through 12.
--- End quote ---
Season 3. :tup:
--- Quote from: Joab on March 22, 2010, 09:53:07 AM ---Great episode! Except with the fact that the detectives did a hat trick.. everything else was great!!
Great Detour choices, great Roadblock!
Self-driving for the entire leg!
Ambiguous clues! The bottle cork and the piece of clue that direct teams to Tattinger. And the Joan of Arc! Very well-planned leg!
I would have personally done the finding the grapes detour... building a pyramid worth of glasses... that's crazy. My respect goes out to Dan and Jordan for even completing that. I even think it's worth giving up 3 race placings to complete a feat like that.
Dan and Jordan were really great to watch this leg. I like the fact that the cowboys deal with setbacks with smiles. The duct tape that Steve used was great! Carol and Brandy were not being b***hes because they were obviously at the front of the pack...
As for Jeff and Jordan elimination... it was overdue. :lol:
--- End quote ---
This week (out of laziness) I will forego my usual rant/opinion about the leg and agree with everything you said. This was a great leg, and it managed to make up for being the second leg in a row without any bunching points. :jumpy:
cosmophobia:
--- Quote from: chill_sd on March 22, 2010, 04:10:42 PM ---
--- Quote from: walkingpneumonia on March 22, 2010, 03:57:43 PM ---I'm still having problems with the math though - how would you calculate this other than drawing it out level by level?
--- End quote ---
There are some shortcuts for adding up triangular numbers, but as you can see from the edit above, I made a small mistake. When I went back, I used a spread sheet to count all the glasses that would be in each row.
A quick explanation of the shortcut: The bottom level would have rows of glasses starting with 1 at the top of the triangle and progressing to 15 at the bottom. The top and bottom rows add up to 16, as do the 2nd and 14th rows. So you have 7 pairs of rows adding up to 16 glasses each pair, and 8 in the middle row. 7 times 16 plus 8 = 120 glasses in the bottom layer.
PS - I would have used a similar trick to add up the numbers on a clock face (I don't remember which season, but it was part of a task involving finding numbers to open a safe). The clock has 12 numbers, which can be paired up 1-12, 2-11, 3-10, 4-9. 5-8 and 6-7. Six pairs that add up to 13. 6 times 13 = 78, which is the sum of the numbers 1 through 12.
--- End quote ---
Oh, it's quicker with a summatory formula. The number you want to add up to, multiplied by its succesor and divide by 2
so: (12x13):2 = 6x13= 78!
I LOVED that switzerland detour.
apskip:
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)
2. You must switch to a square pattern and start the same way with a level 1 square of 9 x 9. Level 2 is 8x8, 64. Level 3 is 7x7, 49. Level 4 is 6x6, 36. Level 5 is 5x5, 25. level 6 is 4x4, 16, level 7 is 3x3, 8. level is 2x2, 4. level 9 is 1. Add them up quickly and you get 819, so level 1 must start with 12 and not 13. then you add them up to get 650. You can't get there from here on this one either.
3. A hybrid approach appears the only one that can work but I have to back off and say that the mathematical closure on this just isn't there. My mistakes in the earlier two approaches led to inaccurate conclusions, but I hope you had some fun trying out your mathematical dexterity. If anyone did better let's hear about it.
The other side of the equation is how to actually stack the glasses. Heresay has it that if you take out one glass from most many levels, the champagne will be able to drain through there. Here is what a professional bartender who has done this trick has been reported about the proper way to do it:
You know that the glasses have to be stacked in a pyramid.
Now here's the trick to filling all the glasses and not pouring your Champagne all over the table top....make sure your glasses are about a fingers width apart all around. If they're touching each other, the Champagne will follow the rims and stems and just dribble all over the place(not good). By keeping the glasses from touching each other, the Wine will follow the stems and bases of the glass just like the little waterfall you want to have.
You won't even need a tray under glasses. No wine will wet the table as long as the glasses are not touching each other.
No doubt there will be those dissatisfied with this analysis. I say you should go out and buy 660 wine glasses and try it out.
I expect all of you will enjoy this demonstration of a tetrahedron shape with about 5000 glasses, which is totally amazing:
http://www.metacafe.com/watch/343130/pyramid_of_glasses/
Try it at your next party.
Dånooky:
--- 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)
2. You must switch to a square pattern and start the same way with a level 1 square of 9 x 9. Level 2 is 8x8, 64. Level 3 is 7x7, 49. Level 4 is 6x6, 36. Level 5 is 5x5, 25. level 6 is 4x4, 16, level 7 is 3x3, 8. level is 2x2, 4. level 9 is 1. Add them up quickly and you get 819, so level 1 must start with 12 and not 13. then you add them up to get 650. You can't get there from here on this one either.
3. A hybrid approach appears the only one that can work but I have to back off and say that the mathematical closure on this just isn't there. My mistakes in the earlier two approaches led to inaccurate conclusions, but I hope you had some fun trying out your mathematical dexterity. If anyone did better let's hear about it.
The other side of the equation is how to actually stack the glasses. Heresay has it that if you take out one glass from most many levels, the champagne will be able to drain through there. Here is what a professional bartender who has done this trick has been reported about the proper way to do it:
You know that the glasses have to be stacked in a pyramid.
Now here's the trick to filling all the glasses and not pouring your Champagne all over the table top....make sure your glasses are about a fingers width apart all around. If they're touching each other, the Champagne will follow the rims and stems and just dribble all over the place(not good). By keeping the glasses from touching each other, the Wine will follow the stems and bases of the glass just like the little waterfall you want to have.
You won't even need a tray under glasses. No wine will wet the table as long as the glasses are not touching each other.
No doubt there will be those dissatisfied with this analysis. I say you should go out and buy 660 wine glasses and try it out.
I expect all of you will enjoy this demonstration of a tetrahedron shape with about 5000 glasses, which is totally amazing:
http://www.metacafe.com/watch/343130/pyramid_of_glasses/
Try it at your next party.
--- End quote ---
Nice geometrical analysis, and I really want to try it myself (with plastic glasses, mind you :lol:). However, considering the average "apparent intelligence" (smarts shown on-screen) of this season's cast, grape-finding was obviously the safest choice. Kudos to the brothers for completing it even though they had to lose 2 positions.
TARAsia Fan:
Grapes may have been the needle in the haystack task, but it certainly led to better efficiency as we found out. As we saw with Brent & Caite that stacking the glasses was practically a disaster waiting to happen. Although Dan & Jordan figured it out and did a great job with it.
I do like the increased self-driving this season and increased difficulty in the clues. Reminds me of the first two seasons. :tup:
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