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# Give a monkey enough rope

## Question

I am giving this puzzle verbatim from a book I read long ago. These days most everything I have ever done was long ago. But I digress. I simply don't trust myself to re-cast it into scintillating banter style. So if its tenor is archaic or arcane, the onus is off me. Enjoy.

A rope ran over a pulley; at one end was a monkey, at the other end a weight. The two remained in equilibrium. The weight of the rope was 4 oz/foot, and the ages of the monkey and the monkey's mother amounted to four years. The weight of the monkey was as many pounds as the monkey's mother was years old, and the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey.

The weight of the weight exceeded the weight of the rope by as many pounds as the monkey was years old when the monkey's mother was twice as old as the monkey's brother was when the monkey's mother was twice half as old as the monkey's brother will be when the monkey's brother is three times as old as the monkey's mother was when the monkey's mother was three times as old as the monkey was in paragraph 1.

The monkey's mother was twice as old as the monkey was when the monkey's mother was half as old as the monkey will be when the monkey is three times as old as the monkey's mother was when the monkey's mother was three times as old as the monkey was in paragraph 1.

The age of the monkey's mother exceeded the age of the monkey's brother by the same amount as the age of the monkey's brother exceeded the age of the monkey.

What was the length of the rope?

Edited by bonanova
Correct error in Paragraph 2.
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## 22 answers to this question

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This has languished for a couple of weeks ...

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para 2 and 3 have the most complex sentences i hav evr seen i even tried reading from the end of the sentence to the beginning hoping it would help.. but no....

Edited by hhh3

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

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since part of the rope (Rm) is on the monkey side of the pulley, and the rest (Rw) is on the weight side, we have two equations:

W + Rm + Rw = 3 * M / 2

W + Rw = M + Rm

From these, we can derive M = 4 * Rm

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i think its

6 ft long

monkeys age plus moms age = 4 years. they cant be both 2 and monkey cant be 0 so mom is 3 and monkey is 1.

monkeys weight =moms age so monkey weighs 3lbs
monkey and weight are equal.
weight of the rope is half the weight of the monkey. so the rope weighs 1 and a half lbs.
at 4 oz/ ft thats 24 oz=6ft.....

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tammie

i think its

6 ft long

monkeys age plus moms age = 4 years. they cant be both 2 and monkey cant be 0 so mom is 3 and monkey is 1.

monkeys weight =moms age so monkey weighs 3lbs
monkey and weight are equal.
weight of the rope is half the weight of the monkey. so the rope weighs 1 and a half lbs.
at 4 oz/ ft thats 24 oz=6ft.....

Great solve, only it made an assumption about the monkeys' ages. The monkeys did all just come from their birthday parties, so the ages are fractional not whole numbers. Give it another try. For helpers, the rope is shorter than your calculation gave.

It is helpful to relate all the statements to the weights of the weight and rope, and the present ages of the three monkeys.

There is enough information to solve for these five parameters.

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ...

Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ...

Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

So the rope has legs and plays footbal?! And monkey's mother is a male?! And age is money?!

Was it Google translation? I guess, it'll be awhile before computers can understand and translate natural language.

Although it's worth noting that about the only bit translated correctly, is that very thing, which I misunderstood. The translation states, the weight of the rope together with the weight is 1.5 times the weight of the monkey, as the problem statement intended. Whereas I understood it as half weight of the monkey.

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ... Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

So the rope has legs and plays footbal?! And monkey's mother is a male?! And age is money?!Was it Google translation? I guess, it'll be awhile before computers can understand and translate natural language.Although it's worth noting that about the only bit translated correctly, is that very thing, which I misunderstood. The translation states, the weight of the rope together with the weight is 1.5 times the weight of the monkey, as the problem statement intended. Whereas I understood it as half weight of the monkey.

I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

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you say the ages are not whole numbers but the statement saying that the age of the monkey`s mother exceeded the age of the monkeys brother by the same amount as the age of the brother exceeds the age of the monkey would suggest that the brother must be 2 years old on the nose as the monkeys age and his mother`s age added up equal 4 years? am i wrong? though i don`t think knowing that will help me much i thought i`d mention it.

ages not whole numbers?

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you say the ages are not whole numbers but the statement saying that the age of the monkey`s mother exceeded the age of the monkeys brother by the same amount as the age of the brother exceeds the age of the monkey would suggest that the brother must be 2 years old on the nose as the monkeys age and his mother`s age added up equal 4 years? am i wrong? though i don`t think knowing that will help me much i thought i`d mention it.

ages not whole numbers?

They can be fractions. 4/3 yrs + 8/3 yrs = 4 years for example.

Let x y z be the present ages of monkey, mother and brother, W be weight of the weight and l/4 be weight of the rope.

Solve for them. Let them be whatever they turn out to be.

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ... Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

So the rope has legs and plays footbal?! And monkey's mother is a male?! And age is money?!Was it Google translation? I guess, it'll be awhile before computers can understand and translate natural language.Although it's worth noting that about the only bit translated correctly, is that very thing, which I misunderstood. The translation states, the weight of the rope together with the weight is 1.5 times the weight of the monkey, as the problem statement intended. Whereas I understood it as half weight of the monkey.
I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

The rope ran over a pulley on one end of a monkey on the other end ves.Dva remaining ravnovesii.Ves war was 4 oz / football, and at the age of monkeys and apes mother was four goda.Ves monkey was a lot of pounds, as a mother monkey was years, and the weight of weight and the weight of the rope together were half as much as the weight of the monkeys.

Weight weight weight exceeded rope as many pounds as a monkey years old when his mother was twice as old as the monkey monkey brother was a mother monkey was twice as old as his brother is a monkey, the monkey when the brother is three times as old as the mother monkey When she was a monkey three times as old as the monkey in paragraph 1.

Mother was twice as old as the monkey monkey monkey When the mother was half as old as the monkey will be when the monkey is three times as old as the mother monkey was when the mother monkey is three times as old as the monkey in paragraph 1.

Maternal age exceeded the age of his brother monkeys monkeys in the same amount as age exceeded the age of his brother monkeys monkeys.

What was the length of the rope?

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The rope ran over a pulley on one end of a monkey on the other end ves.Dva remaining ravnovesii.Ves war was 4 oz / football, and at the age of monkeys and apes mother was four goda.Ves monkey was a lot of pounds, as a mother monkey was years, and the weight of weight and the weight of the rope together were half as much as the weight of the monkeys.

Weight weight weight exceeded rope as many pounds as a monkey years old when his mother was twice as old as the monkey monkey brother was a mother monkey was twice as old as his brother is a monkey, the monkey when the brother is three times as old as the mother monkey When she was a monkey three times as old as the monkey in paragraph 1.

Mother was twice as old as the monkey monkey monkey When the mother was half as old as the monkey will be when the monkey is three times as old as the mother monkey was when the mother monkey is three times as old as the monkey in paragraph 1.

Maternal age exceeded the age of his brother monkeys monkeys in the same amount as age exceeded the age of his brother monkeys monkeys.

What was the length of the rope?

I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

Nice. Whereas one of the two Google founders was born in Moscow.

You must know Russian to appreciate and fully enjoy the beauty of the translation.

The first sentence of the translation actually is: The rope [to] pulley had ran up to ... (As if the rope or pulley had legs and actually ran. Hard to say which.)

Working off the OP in English with some aid of Russian translation I get a very large negative weight for the rope.

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The rope ran over a pulley on one end of a monkey on the other end ves.Dva remaining ravnovesii.Ves war was 4 oz / football, and at the age of monkeys and apes mother was four goda.Ves monkey was a lot of pounds, as a mother monkey was years, and the weight of weight and the weight of the rope together were half as much as the weight of the monkeys.

Weight weight weight exceeded rope as many pounds as a monkey years old when his mother was twice as old as the monkey monkey brother was a mother monkey was twice as old as his brother is a monkey, the monkey when the brother is three times as old as the mother monkey When she was a monkey three times as old as the monkey in paragraph 1.

Mother was twice as old as the monkey monkey monkey When the mother was half as old as the monkey will be when the monkey is three times as old as the mother monkey was when the mother monkey is three times as old as the monkey in paragraph 1.

Maternal age exceeded the age of his brother monkeys monkeys in the same amount as age exceeded the age of his brother monkeys monkeys.

What was the length of the rope?

I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

Nice. Whereas one of the two Google founders was born in Moscow.

You must know Russian to appreciate and fully enjoy the beauty of the translation.

The first sentence of the translation actually is: The rope [to] pulley had ran up to ... (As if the rope or pulley had legs and actually ran. Hard to say which.)

Working off the OP in English with some aid of Russian translation I get a very large negative weight for the rope.

0 for 2 is not bad.

It's positive, and not all that long.

The tricky part is ascribing the right time frames to the numbers.

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I understand, it's more of a language exercise, than math.

Let monkey's age in paragraph 1 be

a.
Then from paragraph 3:
Monkey's mother is 4.5a, when monkey is 2.25a.
Then from paragraph 1: a = 16/17 year. And monkey's mother is 3 and 1/17 years old, same as monkey's weight in pounds. So the weight plus the rope are 4 and 10/17 lb.
From paragraph 4: monkey's brother is 1.125a older than monkey and younger than monkey's mother by the same amount. That difference is 18/17 years, making monkey's brother exactly 2 years old in paragraph 1.
From paragraph 2:
Monkey's age calculates as as 31.5a = 29 and 11/17 years old. And by that many pounds the weight exceeds the rope. Whereas together they weigh just over 4.5 lb.

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I understand, it's more of a language exercise, than math.

Let monkey's age in paragraph 1 be

a.

Then from paragraph 3:

Monkey's mother is 4.5a, when monkey is 2.25a.

Then from paragraph 1: a = 16/17 year. And monkey's mother is 3 and 1/17 years old, same as monkey's weight in pounds. So the weight plus the rope are 4 and 10/17 lb.

From paragraph 4: monkey's brother is 1.125a older than monkey and younger than monkey's mother by the same amount. That difference is 18/17 years, making monkey's brother exactly 2 years old in paragraph 1.

From paragraph 2:

Monkey's age calculates as as 31.5a = 29 and 11/17 years old. And by that many pounds the weight exceeds the rope. Whereas together they weigh just over 4.5 lb.

Nice.

What you have is correct:

a = 16/17

mother = 52/17 = 3 1/7

weight + rope = (3/2)(52/17) = 4 10/17.

brother = 2.

So you navigated paragraph 3 just fine.

Then comes paragraph 2.

What should come out of p2. is Weight = rope + 11(a) - 2(mother)

Does that make sense from the way you read p2?

Two equations to solve.

You're right - it's a puzzle in reading verb tenses or whatever ...

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Somehow, I see paragraph 2 differently.

I see paragraph 2 this way:

weight = rope + 2*(2*3*3a - 1.125a) -2.25a

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Somehow, I see paragraph 2 differently.

I see paragraph 2 this way:

weight = rope + 2*(2*3*3a - 1.125a) -2.25a

When the narrative says "was when," or "will be when,"

denote that time frame by an offset of a, b, c, d ... years.

So "... monkey was years old when (x-a) mother was (y-a)

twice as old as brother was when (z-b) mother was (y-b)

half as old as brother will be when (z-c) brother is (z-c)

three times as old as mother was when (y-d) mother was (y-d)

three times as old as monkey was (x) in paragraph 1.

This says

y-a = 2(z-b)

y-b = (z-c)/2

z-c = 3(y-d)

y-d = 3x

The whole paragraph says W = L/4 + (x-a).

Eliminate a, b, c, d, and use z = (x+y)/2.

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Somehow, I see paragraph 2 differently.

I see paragraph 2 this way:

weight = rope + 2*(2*3*3a - 1.125a) -2.25a

When the narrative says "was when," or "will be when,"

denote that time frame by an offset of a, b, c, d ... years.

So "... monkey was years old when (x-a) mother was (y-a)

twice as old as brother was when (z-b) mother was (y-b)

half as old as brother will be when (z-c) brother is (z-c)

three times as old as mother was when (y-d) mother was (y-d)

three times as old as monkey was (x) in paragraph 1.

This says

y-a = 2(z-b)

y-b = (z-c)/2

z-c = 3(y-d)

y-d = 3x

The whole paragraph says W = L/4 + (x-a).

Eliminate a, b, c, d, and use z = (x+y)/2.

That's not what paragraph 2 says in the OP.

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Somehow, I see paragraph 2 differently.

I see paragraph 2 this way:

weight = rope + 2*(2*3*3a - 1.125a) -2.25a

When the narrative says "was when," or "will be when,"

denote that time frame by an offset of a, b, c, d ... years.

So "... monkey was years old when (x-a) mother was (y-a)

twice as old as brother was when (z-b) mother was (y-b)

half as old as brother will be when (z-c) brother is (z-c)

three times as old as mother was when (y-d) mother was (y-d)

three times as old as monkey was (x) in paragraph 1.

This says

y-a = 2(z-b)

y-b = (z-c)/2

z-c = 3(y-d)

y-d = 3x

The whole paragraph says W = L/4 + (x-a).

Eliminate a, b, c, d, and use z = (x+y)/2.

That's not what paragraph 2 says in the OP.

You're right. OP is corrected.

I was presumptuous to teach you how to solve ...

Apologies.

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Somehow, I see paragraph 2 differently.

I see paragraph 2 this way:

weight = rope + 2*(2*3*3a - 1.125a) -2.25a

When the narrative says "was when," or "will be when,"

denote that time frame by an offset of a, b, c, d ... years.

So "... monkey was years old when (x-a) mother was (y-a)

twice as old as brother was when (z-b) mother was (y-b)

half as old as brother will be when (z-c) brother is (z-c)

three times as old as mother was when (y-d) mother was (y-d)

three times as old as monkey was (x) in paragraph 1.

This says

y-a = 2(z-b)

y-b = (z-c)/2

z-c = 3(y-d)

y-d = 3x

The whole paragraph says W = L/4 + (x-a).

Eliminate a, b, c, d, and use z = (x+y)/2.

That's not what paragraph 2 says in the OP.

You're right. OP is corrected.

I was presumptuous to teach you how to solve ...

Apologies.

Thanks. That brings it closer. I get a positive weight rope now, alas, not enough for the monkey and the rope together to balance the weight.

The way I see paragraph 2 now:

Weight - rope = ((3*3a)/2 -1.125a)*2 - 2.25a = 4.5a. (Where a=16/17).

Whereas, Weight + rope = 4.875a (from paragraph 1). Leaving the weights as 0.1875a for the rope weight, 4.6875a for the weight, and 3.25a for the monkey. Where the monkey together with the entire rope cannot outweigh the weight.

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If "...the weight of the weight and the weight of the rope were together half as much again as the weight of the monkey," how can that system be in equilibrium?

Конечно ... Веревка подбежал шкив, на одном конце была обезьяна, на другом конце вес.Два оставшихся в равновесии.Вес каната было 4 унции / футбол, а в возрасте от обезьяны и мать обезьяны составил четыре года.Вес обезьяна была много фунтов, как мать обезьяны было лет, и весом весом и весом каната вместе были в полтора раза больше, поскольку вес обезьян.

Вес вес превышал вес веревки, как многие фунтов, как обезьяна лет, когда мать обезьяны был вдвое старше брата обезьяны было, когда мать обезьяны был вдвое старше брата обезьяна будет, когда брат обезьяны в три раза стара, как мать обезьяны Когда мама была обезьяна была в три раза стара, как обезьяна в пункте 1.

Мать обезьяны был вдвое старше обезьяна Когда мать обезьяны был наполовину стара, как обезьяна будет Когда обезьяна в три раза стара, как мать обезьяны было, когда мать обезьяны в три раза стара, как обезьяна в пункте 1.

Возраст матери обезьяны превысил возраст брата обезьяны на такую ​​же сумму, как возраст брата обезьяны превысил возраст обезьяны.

Какова была длина веревки?

So the rope has legs and plays footbal?! And monkey's mother is a male?! And age is money?!Was it Google translation? I guess, it'll be awhile before computers can understand and translate natural language.Although it's worth noting that about the only bit translated correctly, is that very thing, which I misunderstood. The translation states, the weight of the rope together with the weight is 1.5 times the weight of the monkey, as the problem statement intended. Whereas I understood it as half weight of the monkey.
I was going to add the caveat that I cannot verify the usefulness of google translate. But yes, I thought all monkeys played football.

Actually now I am convinced the puzzle is broken in paragraph 2.

Trying to fix it, knowing the answer, but I may just close the topic.

Thanks for working on it.

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