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.)

(In reply to My thoughts on solutions and posted solution. by Jer)

My overall intent was to couch this in geometric construction with as few external influences a possible (unfortunately it seems I introduced one - discussed a little later).

Part 2:   
This was the premise upon which the scenario was founded:
"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."

but - the solution does incorrectly read "The plank is longer than the pit radius but is longer than the oblique ....." when it should have read "The plank is shorter..."

Part 3:
"I had assumed the purpose of the second contestant was...."

I should never have introduced a second person but to get the array which I required I always had to assume that at review someone was going to ask "How can one person support two planks and yet get the third in place?"

At this comment I did indicate to broll that I was looking for a weaving solution and broll did again take that on board.  In a further comment I did try to guide the solver towards my thought

"what is an 'icypole stick'?"  Culture!  We speak the same language and yet we don't.   Here in Australia we have "icypoles" you have "popsickles".   No, I did not rename the planks as sticks.  I was merely attempting to offer a solver something within "easy reach" to emulate and confirm the situation.

Bonus.  Apologies, I didn't realise that was broll's intent with the addition of the 2 extra planks; and   
I did intend to offer my solution for this outside the Official solution.

Consider two more planks/sticks similarly interlocked at the end of one of the three in Part 3 to form an array such as  "   >--<  ".

Thanks for the discussion, and clearly there are solutions which are non-gemetric when other influences are allowed.

Posted by brianjn on 2010-04-15 22:18:13