# LR puzzle

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The classic problem of a monkey and the greased flag pole. The height of a certain flag pole is 30 feet. Grease is applied to the pole. A
monkey attempts to climb the pole. It climbs 3 feet every second but slips down 2 ft in the next second. When will the monkey reach the top
of the flag pole?

56 seconds

27 seconds

60 seconds

55 seconds

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First second, it goes up 3 feet, next second it slips down 2, is that correct? If so, it goes up 1 foot every other second. In second 53, it reaches 29 feet, but slips down to 27 the next. The very next second (54), it climbs up the remaining 3 and reach the top.

55 seconds.

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Every 2 seconds it makes a progress of 1ft.Thus 60.But isnt ther a Mathematical model or progression we can model for that

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Every 2 seconds it makes a progress of 1ft.Thus 60.But isnt ther a Mathematical model or progression we can model for that

If it arrived at 1 foot up at 2s; from which direction would it arrive?

If it arrived at the top at 60s; from which direction would it arrive?

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First second, it goes up 3 feet, next second it slips down 2, is that correct? If so, it goes up 1 foot every other second. In second 53, it reaches 29 feet, but slips down to 27 the next. The very next second (54), it climbs up the remaining 3 and reach the top.

55 seconds.

This assumes the monkey occupies virtually no volume. We all know that's not true. Taller monkey = slightly shorter time.

Edited by Mondays Assignment: Die

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This assumes the monkey occupies virtually no volume. We all know that's not true. Taller monkey = slightly shorter time.

Sure, we can also assume the monkey is 30 ft tall, so it reaches the top instantly. It's a brain teaser though, not an experiment. So there's no need to invoke any extra parameters other than what's in the OP.

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I know. I was kidding.

No fun!

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At least one monkey was seriously harmed in this thought experiment.

I agree with pwagen (post #2), assuming that at t=0 s, monkey simply hasn't started and that at t=1 s, he arrived at 3 ft.

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1feet every second so at 27 second 27 ft at the next second it reachs the top.

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the monkey goes up 3 feet, then goes back 2 feet. That means 1 feet any 2 seconds.

It also means that when he will reach the height minus 3feet the next second he will reach the top.

So you have

30-3=27feet

27feet times 2sec/feet = 54sec

54sec +1=55sec

Edited by michel123456

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daniton, on 09 May 2013 - 09:43, said:

1feet every second so at 27 second 27 ft at the next second it reachs the top.

I agree with this answer and a very literal (mis?)interpretation of the puzzle: The monkey is climbing 3 feet "every" second, it doesn't say it stops climbing for alternating seconds (though that's probably what was meant).

It also doesn't imply constant velocity. Reading the puzzle to mean that the monkey climbs 3 feet sometime over every second, and slips 2 feet sometime over every second except the first, it could make it in as little as 26 seconds if it completes the final 3 feet before any slipping in that second, otherwise as long as 28 seconds if it slips before the climb in the final seconds.

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I didn't even see the linguistic problems in the OP until daniton's reply. It seems you can interpret "3 feet every second" and then "down 2 every other second" in (at least) 3 ways:

1. Presumably the "normal" interpretation

3 feet up the first second, down 2 the next second, which would give the answer I gave above.

2. The literal interpretation

Up 3 feet the first second. Up 3 feet the next second, while simultaneously slip down 2. In effect, the monkey climbs 2 feet per second until he reaches 28 feet on second 14 (assuming he slips and climbs at the same time, otherwise he would reach the top in 14 seconds). Then he would reach the top in 14 2/3 seconds.

3. The I have no idea what's going on interpretation

The monkey climbs 3 feet every second. But the second after "every second", he slips down 2 feet. This would mean that he would slip 2 feet down every second, while climbing 3. I don't know where I was going with this, and it looked better in my head, but there you go.

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Imagine the monkey is constantly slipping and constantly propelling himself such that he remains in one spot on the pole. Would you still say he is "climbing" the pole in this situation? Would you still say he is "slipping down" the pole in this situation?

10 seconds.

The word "climb" implies that he is cumulatively ascending or moving along, but "slip down" doesn't imply anything about cumulative motion. In "slip down," the word "down" only implies directionality, not motion, whereas definitions of "climb" usually use the word "ascend" or other words that imply motion.

You don't need to subtract the slip from the climb because the "slip down" is already factored into the cumulative (climbed) distance.

Edited by Mondays Assignment: Die

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The word "climb" implies that he is cumulatively ascending or moving along, but "slip down" doesn't imply anything about cumulative motion. In "slip down," the word "down" only implies directionality, not motion, whereas definitions of "climb" usually use the word "ascend" or other words that imply motion.

You don't need to subtract the slip from the climb because the "slip down" is already factored into the cumulative (climbed) distance.

Climbing 3 feet implies an upward movement of 3 feet (cumulative, not necessarily contiguous or constant), and slipping 2 feet implies a downward movement of 2 feet. It makes no sense to consider these as simultaneous. Ascending 1 foot while slipping is still a climb of 1 foot; why would anyone say the monkey slipped 2 feet if it never lowered in height?, what would the 2 feet mean?

Edit: I think I opened a can of worms bringing up interpretations. Sorry. You could say "The monkey climbed 3 feet while its hands/feet slipped (slid downward) 2 feet (across the surface of the pole)" and that makes sense, but it's not what the puzzle says.

Edited by md65536

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Climbing 3 feet implies an upward movement of 3 feet (cumulative, not necessarily contiguous or constant), and slipping 2 feet implies a downward movement of 2 feet. It makes no sense to consider these as simultaneous. Ascending 1 foot while slipping is still a climb of 1 foot; why would anyone say the monkey slipped 2 feet if it never lowered in height?, what would the 2 feet mean?

You're right. "Down" doesn't imply movement over a distance, but "2 feet" does.

If they aren't simultaneous, he must be alternating between upward and downward motion within each second. However, this doesn't mean the climb value can't express net distance.

On its own, "It climbs 3 feet every second" would imply that, variation aside, the net upward distance for each second is 3 feet. It's the sentence's second clause that makes the whole sentence difficult to interpret.

"It climbs 3 feet every second but slips down 2 ft in the next second."

Hmm, why is "the next second" given the modifier "the" if there are actually multiple "next second"?

Edited by Mondays Assignment: Die

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"It climbs 3 feet every second but slips down 2 ft in the next second."

Hmm, why is "the next second" given the modifier "the" if there are actually multiple "next second"?

It's just the best literal interpretation that I could come up with. It doesn't matter much if it's right because I already know it wasn't the intended interpretation.

The word "next" in "the next second" is relative to "every second".

Every day I go to sleep, and wake up in the next day. Hopefully there are multiple next days.