Gilbert Grape's Dilemma
Gilbert Grape must stack the thirty cases of canned vegetables. Each case contains 24 cans. He wants to display them in a pyramid, with each row containing one less than the row below it. Is it possible to use up all the cans and have a top row with only one can?
How many rows of cans would he have ?
If you are wondering, Gilbert Grape is the clerk who works in Lamson's Grocery !
How many rows of cans would he have ?
If you are wondering, Gilbert Grape is the clerk who works in Lamson's Grocery !
Labels: logic, mathemagic
posted by Rajesh Lal at
8:09 PM
12 Comments:
I don't think this is possible. The largest pyramid he could create would have 37 rows, which would use up 703 cans, and he would have 17 cans left over.
yeah, concur with black night. you'd have 720 cans for your pyramid; 37 rows give you 17 cans left over. not possible with top row having 1 can and the remaining rows having one more can than the row above it.
Is he stacking cases or cans?
I've just had some fun working out some general formula for can-stacking (yes, you can call me a nerd). These are the amounts of cans you need to stack n rows of a pyramid of the given type:
Flat Pyramid (the type asked for in this puzzle - really only a triangle):
1+2+3+...+n = SUM(i=1...n)i = (n+1)n/2
(that's not really from me, some famous mathematician worked that out when he was a kid, can't remember which)
Square Pyramid (with square base):
1²+2²+3²+...+n² = SUM(i=1...n)i² = n(n+1)(2n+1)/6
Tetrahedron (pyramid with triangular base):
1+3+6+10+...+(n+1)n/2 = SUM(i=1...n)(i+1)i/2 = n(n+1)(n+2)/6
Needless to say, none of these formulas turn out to be exactly 720 for any natural n, although Gilbert could sack the 30 cases to a square pyramid with 4 rows ;)
THE QUESTION IS WRONG. IT'S A TRICK QUESTION. IT SAYS THAT AT FIRST HE NEEDS TO STACK THE CASES.BUT LATER ON IT SAYS THAT THERE SHOULD BE 1 CAN AT THE TOP!
BUT HE NEEDS TO STACK THE CASES WHICH HAVE MORE THAN 1!! BUT ONLY ONE CAN SHOULD BE AT THE TOP!!THERE ARE 24 INSIDE 1 CASE SO IT'S IMPOSSIBLE TO ANS!!!
He would only be able to stack 37 rows and have 17 cans left.
kyel, it dosent actually specify stacking cases, and later mentions stacking cans, so everyone just did the smart thing and realized that he meant cans... and please dont type in all caps... it makes you seem more retarded
He stacks 30 cases in 5 rows of a three-sided pyramid, (minus the one case on top), then takes a can from one case and puts it on top. That's "stack the thirty cases" and "have a top row with only one can", which is what was asked for.
This post has been removed by the author.
This post has been removed by the author.
Gilbert Grape must stack the thirty cases of canned vegetables. Each case contains 24 cans. He wants to display them in a pyramid, with each row containing one less than the row below it. Is it possible to use up all the cans and have a top row with only one can?
How many rows of cans would he have ?
If you are wondering, Gilbert Grape is the clerk who works in Lamson's Grocery !
If you interpret it to mean 1 less case in each row, then the cases could be arranged in a square base pyramid. This would amount to a pyramid with 4 cases in the bottom row; as previously mentioned. If the cases were orientated how you might imagine a diamond, such that the cases in the bottom layer were supported only by one point each, then subsequent layers would teselate with crates face to face. This will work with any cuboid shape, and hopefully there will be enough friction to prevent collapse. It also means that the single crate at the top has one corner pointing upward, which will be occupied by a single can, ie 1 can on the top.
This sollution is only really useful for beer as it implies buying whole cases at a time, keeping 24 tins of veg in the cupboard is weird.
The number of cans in a row depends on the layout of the box, maybe 3x4x2. This would mean the longest row of cans (although not horizontal) would be 4 cans x 4 cases = 16.
I like Steve's idea. It works! ("He stacks 30 cases in 5 rows of a three-sided pyramid, (minus the one case on top), then takes a can from one case and puts it on top. That's 'stack the thirty cases' and 'have a top row with only one can', which is what was asked for.")
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