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A Math Puzzle - answered
| Profile | Posted by | Options | Post Date |
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Bob | Report | 19 Mar 2006 13:15 |
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Ants on a Stick - Answer later |
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Bob | Report | 19 Mar 2006 13:15 |
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Ants on a Stick One hundred ants are dropped on a metre stick. Each ant is travelling either to the left or the right with constant speed 1 metre per minute. When two ants meet, they bounce off each other and reverse direction. When an ant reaches an end of the stick, it falls off. At some point all the ants will have fallen off. The time at which this happens will depend on the initial configuration of the ants. Question: over ALL possible initial configurations, what is the longest amount of time that you would need to wait to guarantee that the stick has no more ants? |
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Lynne | Report | 19 Mar 2006 13:47 |
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Bob Do you think we are all mathematical geniuses - LOL!! That is far too hard for me! Lynne |
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Janice | Report | 19 Mar 2006 13:53 |
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1 minute? Janice |
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Mauatthecoast | Report | 19 Mar 2006 14:18 |
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The length of time it takes to shake a stick Bob!! LOL Sorry! Mau ;O))))))))) |
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Researching: |
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Bobtanian | Report | 19 Mar 2006 14:21 |
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to be really, really sure...........two days Bob |
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Researching: |
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Bobtanian | Report | 19 Mar 2006 14:33 |
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give it to one of those gorillas they will eat the bu**ers... |
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Researching: |
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Bob | Report | 19 Mar 2006 17:43 |
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Janice got it right - but was it a guess? The answer is 1 minute! While ants bouncing off each other seems difficult to keep track of, one key idea (fun fact!) makes it quite simple: two ants bouncing off each other is equivalent to two ants that pass through each other, in the sense that the positions of ants in each case are identical. So, you might as well think of all ants acting with independent motions. Viewed in this way, all ants fall off after traversing the length of the stick, i.e., the longest that you would need to wait to ensure that all ants are off is 1 minute. |
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Mauatthecoast | Report | 19 Mar 2006 18:00 |
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Thanks for that Bob. Ahem! Mau ;O)) |
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Researching: |
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Jess Bow Bag | Report | 19 Mar 2006 18:02 |
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Sorry Bob, dont quite understand. can you bring a meter stick and the ants and SHOW me please? Jess x |
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Janice | Report | 23 Mar 2006 22:24 |
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Bob, Sorry for the delay. Only just got round to looking for the answer. I decided the worst-case scenario was if half the ants started from one end and the other half started from the other end then they would meet in the middle and retrace their routes. If any ant made it to halfway, then it couldn't bump into any more because they would be halfway or further so the path would be clear to the far end. Not sure if I've explained that very well lol! I know what I mean!! Janice |
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Jeans Reunited | Report | 23 Mar 2006 22:34 |
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is this relevant. We have a garden pond with some rocks dotted about in the middle. Last summer we noticed that when we put a stick from the side to a rock and then put an ant on the stick, he raced to the other end had a look about and then raced back to the start. He went up to the other ants and then about 6 of them all rushed out to the rock!! Then we moved the stick and they were stuck!!!! lol Claire |
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Janice | Report | 23 Mar 2006 22:36 |
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Claire, How do you know it was a 'he'? lol Janice |
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