The actual math involved here isn’t too difficult; the answer will involving finding the solution to an equation for a given Pyramidal number. I’m pretty sure it was a square pyramid, so the formula is P[sub]n[/sub] = (n(n+1)(2n+ 5-4 [sup]*[/sup])) / 6 .There’s some other information that’s needed (and a few other questions I was thinking about)
How many bowls were said to be needed ? I think it was 30,000 for regular Colon Blow and 2,000,000 for Super Colon Blow. Is that right?
Do these numbers correspond with the height shown in the commercial? I know they don’t show the entire pyramid, but is it possible to see how many layers of bowls there are?
I’m throwing this out there now hoping it’s still fresh in people’s minds and Tivos. (SNL just did another commercial special. And if you haven’t been following any of this, it’s one of the fake commercials from Saturday Night Live, not the actual laxative product which took its name. Further description may be found in the ongoing CS thread.)
*Ack, the one key just died on my keyboard. How annoying. I can’t even get excited about it either. Really, I mean to be upset here. Good thing there’s no factorials involved.
If I’m reading you right, you just want a solution to n(n + 1)(2n + 1))/6 > k. The only real root to the corresponding equation is given by 1/6*(324k+3sqrt(-3+11664k^2))^(1/3)+1/21/((324k+3sqrt(-3+11664*k^2))^(1/3))-1/2, so n has to be greater than that.
For k = 30000, n = 45, and for k = 2000000, n = 182 (rounding up in both cases).
It wasn’t. It looks squarish near the top, but when it moves to SCB you can definitely see that it spreads out faster towards the bottom of the screen.
That makes it interesting. But now that I think about it, I think I do recall seeing that. Was it more like two or three different slopes or does it follow the general curve? Perhaps the SCB pyramid was built underneath the regular Colon Blow pyramid (since he’s already sitting on it).
ultrafilter, that’s one part of it. But I’m also wondering how accurate the depiction in the commercial was.
Let’s assume that a cereal bowl is 6" in diameter and 3" tall (which is probably roughly accurate), and that the two pyramids were square pyramids.
The regular Colon Blow pyramid would be 11’3" tall and 22’6" wide. The Super Colon Blow pyramid would be 45’6" tall and 91’ wide. I don’t think they got the latter one right.
Okay, looking at some of those pictures, the top of the pyramid at least is definitely square. He’s sitting on one at least 7 bowls high. (140 bowl pyramid).
The larger picture is too difficult to make out, but it almost looks like about 30 bowls high, and maybe 15 wide at the top. This would be the bottom of a 45-bowl-high stack (the 30,000 bowls for regular Colon Blow).
It also looks like the bowls are filled and stacked on the cereal in them, so they might be more like 5" or 6" by 6-8" in diameter.
Taking the high side, the regular stack may be as big as 22.5 feet high with a 30’ base, and a 90’ pyramid for Super Colon Blow.
And they do their home improvement with the help of Bigger Hammer Hardware. Just as friendly and helpful as your next door neighbor, but without all that sarcasm that hurts so much.
