[Guest]

i know i misspelled that but i dont feel like clicking there and correcting it lol

ok here it is itsa tough one for people like me but most of you will get it

Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound, and please submit only a single number as your answer.

[Guest]

no one is willing to try it?

[Guest]

i know i misspelled that but i dont feel like clicking there and correcting it lol

ok here it is itsa tough one for people like me but most of you will get it

Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound, and please submit only a single number as your answer.

if each bed can only support 200lbs, and the 200lbs that each bed weighs is distributed evenly (therefore 50lbs thru each leg), the pyramid structure isn't possible.

[Guest]

you can out on as many as you like, though if you want to keep the top bed intact then 200 max

[Prime]

It seems, the bottom layer is already overloaded. 25 beds having to support the weight of 30 at 200 lb each. Am I missing the trick?

[Guest]

each leg can support 200lbs.,therfore the top bed can support 800lbs

i know i misspelled that but i dont feel like clicking there and correcting it lol

ok here it is itsa tough one for people like me but most of you will get it

Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound, and please submit only a single number as your answer.

[Prof. Templeton]

600 pounds

[Guest]

422lbs

[Guest]

Well the guy above kinda ruined it, but I did it anyway before I saw it and here were my steps to solving. At least to finding out how much weight was on the middle most bed initially.

This is going to sound confusing in text, but I'll try anyway. I started making pryamids in reverse order.

First bed is 200

Next 2x2. Each has 1/4 of the top bed

250 - 250

250 - 250

Next is 3x3. It gets a little trickier here. The corner beds will only have 1 leg on them. The side beds will have 2 legs, and the middle will have 4 legs. So the corners are 200 + 1/4* 250. Sides are 200 + 2/4* 250. and middle is 200 + 250

262.5 - 325 - 262.5

325 - 450 - 325

262.5 - 325 - 262.5

Now you could calculate the weight for each bed in the next 4x4, but I knew the middle most of the 5x5 bed would determine the breaking point, and since the middle 2x2 of the 4x4 will be the only legs on top of it, I just worked with the middle 2x2 of the 4x4. Now if you've worked with pyramids before you'll know there's a patter with even rows with even weights like this. I knew this which made it easier. Each of the beds in the 2x2 will have 1 corner of 262.5, 2 corners of 325 each, and 1 corner of 450. So simply add them together. 262.5 + 325 + 325 + 450 = 340.625. Now add the 200 that the bed weighs = 540.625. So now we know the middle 2x2 of the 4x4 is

540.625 - 540.625

540.625 - 540.625

Now this parts easy, because it all depends on the weight of the middle most bed on the bottom 5x5, which will have 4 corners, all of the same weight! (Notice this was the case for the 3x3 with the 2x2 as well.) So now obviously 540.625/4 * 4 corners = 540.625. Add 200 the bed weighs = 740.625. Divide that by the 4 legs the table stands on and we'll see each leg of that table is supporting 185.1563 lbs.

I'll let someone else go about determining how much weight will max it out.

[Guest]

The answer is simple ...

800 Pounds

If you put more than 800 pound the topmost bed's leg will collapse.

The structure if is put in a pyramid structure can go much much higher ... am not computing that since the question states that it is a 5 layered pyramid structure and "how many pounds can you place on top of the topmost bed?"

Here we are assuming that a bed can withstand 200x4 pound extra weight

[Guest]

i know i misspelled that but i dont feel like clicking there and correcting it lol

Misspelled what? If you know you misspelled something, it doesn't take a whole lot of effort to correct it.

ok here it is itsa tough one for people like me but most of you will get it

The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

This structure can't be built. Let's start at the top. The top bed must have four beds below it. Those four beds must be resting on sixteen. Those sixteen beds must be resting on sixty-four.

[Guest]

If my math is right you can add a lot of weight before you stress out the bottom layer center bed. But you can only ad 600 pounds before you break the legs of the top bed.

[Guest]

Well, my math wasn't right.

if you add 105.5555 pounds to the top bed you put exactly 800 pound onto the center bottom bed. According to the puzzel, any more will break the legs of the bottom bed.

[Prime]

It seems, the bottom layer is already overloaded. 25 beds having to support the weight of 30 at 200 lb each. Am I missing the trick?

Oh, I see. Each leg can support 200 lb, not each bed. Then taking into account that each leg already supports 50 lb. of its own bed weight to begin with, the answer is

additional 422 lb. can be loaded on the top bed. (Rounded down).

[Guest]

Misspelled what? If you know you misspelled something, it doesn't take a whole lot of effort to correct it.

This structure can't be built. Let's start at the top. The top bed must have four beds below it. Those four beds must be resting on sixteen. Those sixteen beds must be resting on sixty-four.

It can be built. The top is 1x1, the next row is 2x2, the next 3x3, 4x4, 5x5. It clearly states all beds must be resting on 4 below it. That doesn't mean powers of 4.

[Guest]

the next row is 2x2, the next 3x3

It clearly states all beds must be resting on 4 below it.

If one layer is 2x2 (4 beds), how can the layer below it be 3x3 (9 beds)? If each bed is resting on four below it (one leg on each bed), can you explain how four beds are resting on nine?

[Guest]

If one layer is 2x2 (4 beds), how can the layer below it be 3x3 (9 beds)? If each bed is resting on four below it (one leg on each bed), can you explain how four beds are resting on nine?

I'm not sure what you don't understand. Build a pyramid with blocks. You will see each block touches 4 blocks below it.

1 2 3

4 5 6

7 8 9

1 2

3 4

On the 2x2 bed, bed one is in the center of 1, 2, 4, 5. Bed 2 is in the center of 2, 3, 5, 6. Bed 3 is in the center of 4, 5, 7, 8. Bed 4 is in the center of 5, 6, 8, 9. The middle bed of the 3x3 would have 4 different legs on top of it, one from each of the 2x2. The side beds would have 2 legs (top, bottom, left, right) and the corners woul have one leg. 4 + 4*2 + 1*4 = 16 legs from the 2x2. Make more sense?

[Guest]

I'm not sure what you don't understand.

"They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed."

What do you interpret "one leg on each bed" to mean?

[Guest]

"They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed."

What do you interpret "one leg on each bed" to mean?

I interpret it to mean just what it says. Each bed has 4 legs, and each leg must rest upon a different bed below it. It doesn't say each bed can ony have 1 leg resting upon IT.

[Guest]

"They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed."

What do you interpret "one leg on each bed" to mean?

I interpret it to mean just what it says. Each bed has 4 legs, and each leg must rest upon a different bed below it. It doesn't say each bed can ony have 1 leg resting upon IT.

In the clause "one leg on each bed", "one leg" clearly refers to the first mention of a bed. Therefore when they are resting "on each bed" they must be referring to each of the four beds below. This means that the statement says nothing about how many legs can be on top of a bed.

If it did then the original statement would be very strange, as the author would be jumping from talking about a bed resting on 4 other beds to all of the sudden discussing how many legs can be on top of itself.

[Guest]

It is simple, The maximum weight you can put on top is 600. The base can support about 20,000 pounds and the body of the pyramid is nowhere near that weight, but put over 600 pounds on the top of the pyramid and the bed at the top will collapse because it is carrying 200 pounds of its own weight already.

Edited August 17, 2008 by SoKrisky

[Guest]

422 2/9 lbs. So 422, taking the directions into account.

[Guest]

The weight should not be more than 422.2222 lbs and below is my explanation.

5_stack_bed.pdf

Not sure is this correct?