WEIGHTING GAME

Still puzzling over that monkey puzzle?

Probably not, since no one other than Good Dog (see the comments to yesterday's post) gave - if you'll pardon the phrase - a monkeys!

But that isn't going to deter me!

You will recall that I asked for your solutions to Lewis Carroll's puzzle about the Monkey and the Weight:

A weightless and perfectly flexible rope is hung over a weightless, frictionless pulley attached to the roof of a building.

At one end is a weight which exactly counterbalances a monkey at the other end.

If the monkey begins to climb, what will happen to the weight?

Good Dog decided that first the monkey would 'sink' (go down) but then amended this to a belief that the weight and the monkey would both rise up towards the pulley...

GD's bafflement is not surprising, many mathematical minds have been tested by this puzzle: in his diary entry for December 21 1893, Lewis Carroll's alter ego, C L Dodgson, wrote with evident delight:

Got Prof Clifton's answer to the 'Monkey and Weight' problem. It is very curious, the different views taken by good mathematicians. Price says the weight goes up, increasing velocity. Clifton (and Harcourt) that it goes up, at the same rate as the monkey, while Samson says that it goes down!

In the posthumously-compiled Lewis Carroll Picture Book, the Reverend Arthur Brook was quoted as saying that "the weight remains stationary".

Then, in 1914, Sam Lloyd included the puzzle in his Cyclopedia of 5000 Puzzles, Tricks and Conundrums erroneously concluding that as the monkey climbs the rope he will fall with increasing speed.

The American mathematician writing in 1956 in Scientific American complained about the wording of the puzzle: "One of the difficulties in this tricky problem is that it is not well defined. For example, does the monkey jerk the rope? Or does he begin pulling on it very gently, and if so, how does he maintain the pull?"

You read the whole of Warren Weaver's fascinating article on Carroll the mathematician here, but his questions about the 'Monkey and the Weight' puzzle are in fact, irrelevant.

The correct solution is as follows...

Regardless of how the monkey climbs the rope, the monkey and the weight always remain opposite one another. There is nothing the monkey can do to get above or below it at any time, whether climbing ever so slowly or with frenetic leaps and jerks.

So, now you know! And well done Good Dog -- I think...