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# Classic - Ant and Honey problem

## Question

In a rectangular box, with length 30 inches and height and width 12 inches, an ant is located on the middle of one side 1 inch from the bottom of the box.

There is a drop of honey at the opposite side of the box, on the middle of one side, 1 inch from the top.

What is the shortest distance the ant would need to crawl to get the honey?

Here is a picture that illustrates the position of the ant and the honey.

## Recommended Posts

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One innovative answer, I can think of is honey drop fall off the wall to floor, so did the ant and thus ant has to crawl only 30 inches...

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42 ? (1+30+11) The diagonal route would bring about an inch more.

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my calculations were off. (forgot a six)

I would say 42.

Edited by MikeD
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Wow, nice one MikeD, care to explain ?

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Wow, nice one MikeD, care to explain ?

42 ? (1+30+11) The diagonal route would bring about an inch more.

Could it be so simple....? I think there should be some complexity.....! Still trying to work out......!
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I've got it to sqr(1687) or slightly over 41 inches

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My first answer was totally wrong. I blame my flu meds.

i got 40 inches. That making the poor ant walk on the floor, side wall and ceiling.

sqrt(322 + 242)

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40' flatten the box. (i'm assuming it has a top) 6+12+6=24 -- 1+30+1=32 connect the two points diagonally you get 40'

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MikeD is correct..... I misread and thought the ant and the honey were on the outside of the box (so it couldn't crawl on the floor)

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My first answer was totally wrong. I blame my flu meds.

i got 40 inches. That making the poor ant walk on the floor, side wall and ceiling.

sqrt(322 + 242)

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it would be 42 inches either way the ant goes... up = 11+30+1=42 .... down = 1+30+11=42

Edited by pattie-mae
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I could not think of any other route shorter than 42 inch. However if

we assume that the aunt will fall on to the floor, from its present location, it will have to crawle 1 inch lesser, i.e. 41 inch.

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Ok there's nothing falling down, right ? They're both inside the box and the honey isnt moving, the ant is. Can someone please explain how would the movement go with your 40inch path ? I simply dont get it. May be ok mathemathically (altho i dont see where you get 6+12+6 nor 1+30+1) but can you elaborate on the actual movement? Again floor and ceiling in the same path sorta dont make sence, it would be either one or the other from my p.o.v.

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That's exactly what I was going to say.....(but my picture wasn't as nice as yours and it wouldn't download)

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assuming it's a flying ant, then it could fly the length of the diagonal for a 30 by 10 inch rectangle and travel just 31.6 inches.

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That's exactly what I was going to say.....(but my picture wasn't as nice as yours and it wouldn't download)

But it is nowhere mentioned in OP that the box will be broken for fascilitating the ant.

I hope my logic given in Post # 13, may be the correct answer to this tricky puzzle.

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The box wasnt broken, friend. They just did it to demonstrate the solution, which i do belive is the fastest. Obviously you cant have anything dropping down or flying ants.

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I undersatnd you people had got the answer... you are real genuises... but I would like to put here again explanation for others...

If the ant crawls 1 inch down, then 30 inches across the bottom, then 11 inches up, it will travel 42 inches. But this is not the shortest distance. The solution is found by unfolding the box and then finding the shortest path between the ant and the honey. There are actually 4 ways to "flatten" the box (shown here). But only one method corresponds to the the shortest distance as follows:

The 4th figure corresponds to correct answer: sqrt(322 + 242) = 4 sqrt(82 + 62) = 4 x 10 = 40.

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I undersatnd you people had got the answer... you are real genuises... but I would like to put here again explanation for others...

If the ant crawls 1 inch down, then 30 inches across the bottom, then 11 inches up, it will travel 42 inches. But this is not the shortest distance. The solution is found by unfolding the box and then finding the shortest path between the ant and the honey. There are actually 4 ways to "flatten" the box (shown here). But only one method corresponds to the the shortest distance as follows:

The 4th figure corresponds to correct answer: sqrt(322 + 242) = 4 sqrt(82 + 62) = 4 x 10 = 40.

Got it. Real good puzzle. Thank you.
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41.66 ???

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31 inches(1 inch to crawl to bottom + 30 across the lngth of the box.) The honey drop will be at the bottom of the box by the time the ant reaches there...

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