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The Leadman was instructed that on each floor level of the building under construction, there shall be two workers assigned to do some job. There are seven workers on the ground floor and five workers on the 5th floor.There is no available elevator, stairs or ladders but the workers can use the structural bars attached to a column to go up on 1st floor. To access other floors they can use a jumplift platform suspended at the middle by a strong rope. It works by reversible exchange of potential energy . When two men step and stand on one side of the platform then a man from 5th floor jumps down and land on the other side of the platform, the two men will be lifted up to the 3rd floor while the jumper steps on 1st floor. That is P.E. = 1W x 4H = 2W x 2H (all workers weighs the same and floors have same heights).The rope can withstand the impact of ten workers from a floor but nobody is allowed to climb the rope for safety reason. How should the Leadman perform his task with minimal stunts using the jumplift platform?

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The minimal number of needed stunts is

3

This can be done in the following manner:

We can start with one person from floor 5 jumping down to bring 2 people from floor 1 to floor 3.
Next we can let someone else from floor 5 jump down to get 4 people from floor 1 to floor 2.
Then two people from floor 2 and 1 person from floor 5 should coordinate their jumps such that they land on the platform at the same moment, and they use this to catapult 2 people to floor 4.
Finally we can let two more people climb up to floor 1 and we are done.

This is also optimal, because:

Well, there are three floors that can only be visited by using the platform, and we somehow need to get some people there. So 3 stunts is clearly optimal.

Old Answer (not taking into account the rope strength)

The minimal number of needed stunts is

3

This can be done in the following manner:

First 4 people step on the platform from floor 1, and 3 workers jump down at the same time from floor 5. This results in the 4 people reaching floor 4.
Next, the 3 people that just jumped down two floor 1 can stay there for a moment, while two people from floor 4 jump down again. This results in the three workers being catapulted to the 3rd floor.
Again the two people that just jumped onto the platform can stay there while one person gets down from the 3rd floor. Then two people are lifted to the second floor.
All that is now needed is for one more person to climb up from the ground floor the the 1st floor, and then every floor contains 2 people!

This is also optimal, because:

Well, there are three floors that can only be visited by using the platform, and we somehow need to get some people there. So 3 stunts is clearly optimal.

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  • $\begingroup$ Yes thats the way to arrange it.. while theres another way to do it without breaking the rope strength of 10WH.. the first jump from above solution is12WH. $\endgroup$ – TSLF Aug 25 at 4:28

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