Can you solve this conundrum?

Question

This is really difficult for me to figure out so maybe some of you smarties can help...

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.

Answer 1

the answer is 600 pounds. here is why:

the top bed can only hold 200 pounds per leg. the bed already weighs 200 pounds, so that means evenly distributed, the bed's legs already have 50 pounds on them each from the weight of the bed itself. that means you can put another 150 pounds more on each leg which means 150*4=600 pounds. you can put 600 pounds on top of the top bed and it would even out to be a full 200 pounds rested on each leg of the top bed.....

if the question were how much weight could you put on top of the pile if the BOTTOM MOST BEDS LEGS could only hold 200/each, then the answer would be 14,000 pounds.  

Answer 2

800 pounds...!

Answer 3

200

Answer 4

none, if you you add another pound on top the base layer cant support it

edit:

sorry I misunderstood the question

tables /#of legs on top / weight on top of each table

* * * * * 1 2 2 2 1 : 66.40 153.12 173.43 153.12 66.40

* * * * * 2 4 4 4 2 : 153.1 276.95 326.56 276.95 153.1

* * * * * 2 4 4 4 2 : 173.4 297.26 459.37 297.26 173.4

* * * * * 2 4 4 4 2 : 153.1 276.95 326.56 276.95 153.1

* * * * * 1 2 2 2 1 : 66.40 153.12 173.43 153.12 66.40

* * * * 1 2 2 1 : 65.625 146.875 146.875 65.625

* * * * 2 4 4 2 : 146.875 259.376 259.375 146.875

* * * * 2 4 4 2 : 146.875 259.376 259.375 146.875

* * * * 1 2 2 1 : 65.625 146.875 146.875 65.625

* * * 1 2 1 : 62.5 125 62.5

* * * 2 4 2 :125 250 125

* * * 1 2 1 : 62.5 125 62.5

* * 1 1 : 50 50

* * 1 1 : 50 50

*

answer: 340.62

Answer 5

If it's in the form of a pyramid, it's the middle bed of the base layer (the 5 by 5 layer)...that is the third row...third bed that is always supporting the maximum weight...it first holds one leg of each of four beds on top of it (4 by 4), then a whole bed on top of that, therefore 4 legs again(3 by 3). then again it holds one leg of each of four beds (2 by 2) and then a whole bed again with four legs..you add them up.....(4 + 4 + 4 + 4) times 50 = 800  (we use 50 because each bed with 4 legs weighs 200, therefore 200 / 4 = 50. Each leg weighs 50 pounds).  Therefore 800 pounds is what  it's holding at the moment and this is the maximum it can hold...as the base bed has 4 legs that can hold 200 pounds each = 4 * 2 = 800.

It cannot hold anymore.

I think what makes it confusing is the fact that the bed with 4 legs weighs 200 pounds, that means each leg weighs 50 pounds...but each leg can hold 200 pounds. :)

Answer 6

"each bed leg can only support 200 pounds"

if there is only one bed on top, with four legs....

4x200=800