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 weaving by broll)

Unsure that I quite get this.


Let try a rough ascii sketch:

                           *    |   x
                               *
                         x      | *
                   x            |     * 
              x                 |         *

Here "|" passes over the "*" plank but interlocks/weaves with the "x".

This effectively creates a "diving board" or cantilever.

Let's consider the diameter, 12 feet to be the base of an isosceles triangle. For the apex to lie on the circumference the other two side would need to be just over 8.48 feet.

I was worried about my solution, this was a great piece of lateral thinking but please do reconsider your premise. 

'Weaving planks?'  Hm?

Edited on April 14, 2010, 10:28 am

Posted by brianjn on 2010-04-14 06:44:40