A games program was inspired by the exploits of "Indiana Jones", naturally modifications were made.

In one set of three events a pair of contestants had to retrieve a "gem".

Within the arena the pair would see a deep circular pit, the only aids allowed to enable their task, their 'prize' and any transformations made to the pit for each scenario.

Scenarios of the three distinct events:
In each case a pit of radius 6 feet has the "gem" dangling over its centre at just above head height as the contestants stand at the edge of the pit. Lightweight, anti-slip aluminium planks are presented as their only aids.
1. The top of a column, 1 foot in diameter, is horizontal to the pit opening and in the very centre of the pit. Two planks, length of 5 feet, are available.
2. The height of the column (in #1) is raised 2 feet above the pit opening. Just one 6 foot plank is available.
3. Only three planks are available and they are 8 feet long, there is no column!

[Bonus] Now it would seem that five planks of about 5 feet in length might also accomplish the task as at #3. How might those be arranged?
Note:
1. Jumping is disallowed and not necessary,
2. Measurements
- for a metric reader's perspectivity multiply each foot by 30.5 cm,
- planks are a little longer than one might expect (but that would be necessary in a real situation), and
3. Disregard plank thickness as it has no bearing within the spirit of the exercise.
(4. In a "real world" situation the partner would only be required for #3, thus two contestants.)

Scenario 1 is taken care of. 
Scenario 2 is not.  Corey has a possibly reasonable solution if one of the contestants is strong enough relative to the others weight.   The official solution seems to point out that the 6 foot plank is long enough to reach but doesn't explain how.

Because the column is a foot wide, the gap is really only 5.5 feet at a height of 2 feet.   5.5^2 + 2^2 < 6^2  In fact this diagonal distance is only about 5.85 feet.

Scenario 3 is solved by broll in his second comment which I copied and pasted here:

However there is also another possibility. Place plank 1 as earlier indicated. Place one end of plank 2 on the midpoint of plank 1 and the other on some point on the edge of the pit (this is what I meant to say before). The midpoint of plank 2 would then be more than halfway towards the centre. So plank 3 could be placed from edge to centre resting on the edge and the midpoint of plank 2. If the heavier of the 2 team members then stands on the edgeward end of this 'diving board' the other will be able to walk the plank to the centre and collect the gem. Is this solution allowable?

This seems allowable to me.  I had assumed the purpose of the second contestant was to stand on one end so the other could walk the plank.

brianjn dismisses broll's first solution which involves weaving as 'lateral thinking.'  I think this solution is also allowable.  It is almost requested as the note tells us to disregard plank thickness.  If the planks were thick, such weaving would cause planks to stick up at an angle.

What really bothers me is the official solution.  For one thing, what is an 'icypole stick'?  I assume you just renamed this to plank.  For another this solution involves weaving: the very thing you didn't like in broll's solution.

For the bonus.  The official solution does not offer a solution.  broll has a workable one involving weaving, however, the cantilever is very short (.146 feet) meaning the planks would really have to have next to no thickness and be very strong.  I'm not saying I don't like this solution I just wonder is a non-weaving one exists as it does for the others.

 

Posted by Jer on 2010-04-15 11:20:21