The source of this puzzle is John Derbyshire:THE MONKEY’S MOTHERA 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?

Is it 5 feet?I have found the age of the mother to be 2.5 years. Is it right?

Out of interest, is this the right answer?

Will post answer soon. sorry, busy.

The puzzle is “easily” solved by observing that the difference in age is a constant. The trick is then to write all the conditions starting from the last one and going backwards. Thus, let’s call Y(t)=mother’s age at time t X(t)=monkey’s age at time twe can write something like:Y(0)=3X(0)X(1)=3Y(0)Y(2)=0.5X(1)Y(3)=2X(2)With the conditions:Y(t)-X(t)=2X(0)=constantY(3)+X(3)=4 yrWe are looking for Y(3).It turns out that X(0)=0.5 yr and Y(3)=2.5 yrIf “half as much again” means 1.5 then:Pr=0.5PwPr=weight ropePw=weight weightPm=weight monkeyBut, Pw=Pm so Pr=0.5Pm=0.5Y(3)=1.25 pounds=20 oz Therefore, L=20/4=5 feet.

"It turns out that X(0)=0.5 yr and Y(3)=2.5 yrIf “half as much again” means 1.5 then:Pr=0.5Pw"Arrrghhhh! If you knew the time I spent getting stuck and multiplying a zero....I will mail your solution to the author and get his confirmation.

QuoteOriginally posted by: giupetThe trick is then to write all the conditions starting from the last one and going backwards.The real trick is doing that before your brain turns to mush!P

Dear giupet,QuoteWe are not worthy! We are not worthy! Wayne & GarthThe answer from the author John Derbyshire"Yes. Here is my worked solution--same method as yours [giupet's].First I have written out the problem again, with the sentences numbered forreference.THE MONKEY'S MOTHER-------------------<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 asold as the monkey will be when the monkey is three times as old as themother 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 muchagain as the difference between twice the weight of the weight and theweight 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 yourattention was scrambled from reading <7>. From <3> you know that the weightof the weight IS EQUAL TO the weight of the monkey, so you can freelysubstitute 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 trickis 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..." thereforemeans: "When Junior is 4.5D."---"When the mother was half as old as the monkey will be..." thereforemeans: "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: "Momis 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 my analysis of <8> up above, I showed that L=2W. Therefore L=5.Best wishes,John Derbyshireolimu@optonline.nethttp://www.olimu.com"Mr. Derbyshire was impressed.