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How long is the rope?

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Level 13 Human pita
Alignment: True neutral
Posted on October 3, 2005 at 9:26 pm

A rope hangs over a pulley. On one end is a weight. Balanced on the other end is a monkey of equal weight. The rope weighs 4oz. per foot. The age of the monkey and the age of its mother together equal 4 years. The weight of the monkey is as many pounds as its mother is years old. The mother is twice as old as the monkey was when the mother was half as old as the monkey will be when the monkey is three times as old as the mother was when the mother was three times as old as the monkey. The weight of the weight plus the weight of the rope is half as much again as the difference between twice the weight of the weight and the weight of the monkey. How long is the rope?

Level 13 Extraplanar Programmer
Alignment: Chaotic good
Location: Toronto
Posted on October 3, 2005 at 10:42 pm

I'm a little confused as to what "half as much again" means, but my guess is 12 feet (granted, I'm not very good at these things).

Level 13 Human gamer
Alignment: True neutral
Posted on October 4, 2005 at 12:16 pm

Loooooooooooooooooooooooooooooooooooooooooooooooooooooooooong is my guess.

Level 13 Human Shadow
Alignment: Chaotic good
Location: Earth Orbit, Preparing to Attack
Posted on October 4, 2005 at 12:42 pm

One "kong" in length?

Level 13 Human gamer
Alignment: Chaotic evil
Posted on October 4, 2005 at 6:31 pm

42? :mrgreen:

Level 13 Human pita
Alignment: True neutral
Posted on October 4, 2005 at 8:36 pm

I'm a little confused as to what "half as much again" means

That would be 50% more


one more day then I'll post the answer
:D

Level 13 Human gamer
Alignment: True neutral
Posted on October 4, 2005 at 8:57 pm

10 feet

Level 13 Human gamer
Alignment: Chaotic evil
Posted on October 4, 2005 at 9:20 pm

That's not right... it's 120 inches... or approximately 304.8 centimeters :P

Level 13 Extraplanar Programmer
Alignment: Chaotic good
Location: Toronto
Posted on October 5, 2005 at 12:00 pm

That would be 50% more


one more day then I'll post the answer
:D

Oh, half and again. Well, that probably threw off my calculations a bit. Maybe I'll try again later today.

Level 13 Human Unaffiliated Game Maker
Alignment: Chaotic
Location: England
Posted on October 5, 2005 at 2:46 pm

I honestly didn't even read the whole puzzle... :oops:

Level 13 Human pita
Alignment: True neutral
Posted on October 5, 2005 at 10:30 pm

<1> A rope hangs over a pulley.

<2> On one end is a weight.

<3> Balanced on the other end is a monkey of equal weight.

<4> The rope weighs 4oz. per foot.

<5> The age of the monkey and the age of its mother together equal 4 years.

<6> The weight of the monkey is as many pounds as its mother is years old.

<7> The mother is twice as old as the monkey was when the mother was half as old as the monkey will be when the monkey is three times as old as the mother was when the mother was three times as old as the monkey.

<8> The weight of the weight plus the weight of the rope is half as much again as the difference between twice the weight of the weight and the weight of the monkey.

<9> How long is the rope?

SOLUTION

Suppose the rope is L feet long. There go 16 oz. to the pound, so by <4> the rope weighs 0.25L lbs.

Sentence <8> is almost pure bluff. You don't notice this because your attention was scrambled from reading <7>. From <3> you know that the weight of the weight IS EQUAL TO the weight of the monkey, so you can freely substitute the one for the other. Calling the weight of the weight W, sentence <8> boils down to: W + 0.25L = 1.5W. Rearranging: L=2W.

Now tackle <7>, using D for the difference in ages. (Which, of course, never changes. You will NEVER catch up with your older sister!) The trick is to work backwards from the end of the sentence.

— "When the mother was three times as old as the monkey" can only mean: "When Mom was 1.5D and Junior was 0.5D."

— "When the monkey is three times as old as the mother was..." therefore means: "When Junior is 4.5D."

— "When the mother was half as old as the monkey will be..." therefore means: "When Mom was 2.25D."

— At that point in time, Junior was of course 1.25D.

— "The mother is twice as old as the monkey was..." therefore means: "Mom is currently 2.5D."

— It follows that Junior is currently 1.5D.

— Since, from <5>, these have to add up to 4, D must be 1.

— And from <6>, W is 2.5 lbs.

— In the analysis of <8> up above, It is shown that L=2W. Therefore L=5. The rope is 5 feet long.