Saturday, 5 July 2008

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...

13 comments:

Good Dog said...

Originally I was thinking that if the monkey climbed say 2x per go (where x is a unit of measurement) he would drop back 1x as the two sides evened themselves up....

Oh look, I've run out of paint and not even got to the corner yet.

Thanks for putting me out of my misery. Thankfully, I guess I'm not the Alan Davies.

Brian Sibley said...

Can't remember whether of not you're an Arsenal supporter... But, no, I don't think you're likely to be asked to compile The SECOND Book of General Ignorance! :-)

I happily confess that when I first came across this puzzle some years ago - in an excellent, but now out-of-print, book The Magic of Lewis Carroll by John Fisher - I thought of every permutation but the correct one.

Mind you, if you fed the monkey a banana it would be a whole different game...

Andy J. Latham said...

Ahhh but aren't we ignoring the likely event of the monkey flinging poo? That would reduce it's weight!

Brian Sibley said...

I thought that but you had to go and say it, Andy, didn't you?! :-)

Good Dog said...

An Arsenal supporter? I'm afraid my last comment about Euro 2008 was, "that football pitch is a waste of nine croquet lawns!" That pretty much nails my colours to the mast.

Brian Sibley said...

Excellent! I did hope that (unlike Mr Davies) you wouldn't be a follower of pig's-bladder-kicking, but one never knows. I've got perfectly decent friends who love it...

But, CROQUET! Now you're talking! And, of course, Messrs Carroll and Dodgson and The Queen of Hearts would thoroughly approve! :-)

LisaH said...

Are you suggesting there's anything wrong in having an interest in football, Brian?

Henrik Larsson rules!

Brian Sibley said...

Wouldn't dream of it, Lisah! Another dear friend, GILL (the confident of the Duchess) is also a follower of the game - otherwise she, like you, is very nice! ;-)

Good Dog said...

I must point out that no hedgehogs or flamingos were harmed in any of the games I played.

Having treated myself to the 2-disc Lilo & Stitch on the way home to watch while waiting for the results of the monkey test, I think experiment 626 would make a great ball in what would be a very interesting match.

The second disc documentary seemed to ramble all over the shop to begin with, but when it came to the footage of the original third-act chase... Oh, boy.

Brian Sibley said...

Really liked Lilo & Stitch, must get it...

LisaH said...

So you can't be a football follower and be nice?

Just because some supposed fans attempt to murder each other, chant disgusting things from the terraces and try to rearrange towns when visiting them no need to suggest that it's generally not nice to be interested in the game.

Admittedly I'm a Scottish football fan and by own admission that's a form of mashochism, particularly when watching the national side (a bit like watching England these days, come to think of it) but it can still be done in a genteelish fashion.

Brian Sibley said...

I wasn't saying.......

I didn't mean...............

Oh, bother! Never discuss religion, politics or SPORT!! :-)

LisaH said...

lol