81 thoughts on “Puzzle: Mathematical Ants Solution”

  1. Lets say that all the ants are paired so that they're facing towards each other. After about a secound, they all collide switching directions and two ants fall off. The ants are once again all paired facing eachother but there are now two less ants with more space between them. When this is repeated until the the last two ants fall off, would it not have taken over a minute since the last two ants had to backtrack numerous times?

  2. I feel insulted and enlightened at the same time!
    Insulted coz I just realized how simple it was.
    Enlightened coz I learnt something! HAZZA! 😀

  3. @sushicartman01 That is what I was thinking, the first ants would fall off near instantaneously, and the last ants would fall off sometime in the future (i never bothered to do the math, just a bit of a mental picture). It makes sense, though, that if they were to pass through one another it would take between 30s and 1m….

  4. @SaiyanKirby right forgot that was the original puzzle. Then i had gotten the answer right in the other video (Well aside from the fact that i did minutes vs seconds. but it still had sixty minutes vs 60 seconds and 30 minutes vs 30 seconds. So although my time was incorrect My answer was right.)

  5. Amazing,i would never know.
    BTW I love your ending "If you are happy,thanks for watching"
    I am always happy when watching your videos! 🙂

  6. But isn't the time for colliding shorter than the time it needs to actually get through each other? .. In the "walking through each other" part, there is extra length which is the diameter of the ball! .. Please tell me if I'm wrong! .. I enjoy your videos! 😀

  7. It took me a few seconds to figure out a minute or less, but I thought there was an exact answer so I wracked my brain for like 3 whole minutes trying to figure it out before i watched the vid lol

  8. it really makes no difference, 30s to a minute is virtually what everybody said anyway, i was really expecting a different answer

  9. Now hold on just a minute.

    The two ants at 0 and 100 centimeters are ALREADY at the ends and thus have walked off the stick by default to begin with, regardless of what way they were facing.
    In other words, it will take LESS than one minute at most.

    Unless you assume that an ant at the end is facing towards the stick and that somehow keeps her from falling off. And i say her, since male ants have wings and would fly away anyway.

  10. Ok one second .. if the ants walk and turn around when they run into another and you said thats like if they "passed throug each other" but if they walked through each other then there would be a 0 > X < 1 point at which the ants would be inside each other .. now if we sat the ants in a repeating 0,1 order (0 facing left and 1 facing right) meaning that the ants in the middle couldnt move untill the ants on the sides got facing the right(as in not wrong) side.

  11. Ok one second .. if the ants walk and turn around when they run into another and you said thats like if they "passed throug each other" but if they walked through each other then there would be a 0 > X < 1 point at which the ants would be inside each other .. now if we sat the ants in a repeating 0,1 order (0 facing left and 1 facing right) meaning that the ants in the middle couldnt move untill the ants on the sides got facing the right(as in not wrong) side.

  12. You would expect the answer to be really complicated and when you see the answer you wish you would have figured it out for yourself…

  13. @Amphibiot I believe they have to fall off the ends. And if the ant at 0 is facing right, it has to go all the way across.

  14. @Jiefyang We've got ants that take up no space and have instantaneous collisions. This means that they take absolutely no time to turn around. Because of this, it would be impossible to tell whether a collision had happened or whether they had walked through (or even beside) each other. These would be the "ghost" ants that walk through each other in all practicality

  15. Is this reasoning correct? The number of "ant permutations" to get all the ants to face towards their respective end of the cane is, in the worst case, 100.
    Since they're evenly spaced and the collision takes no time, I only have to calculate the time it takes them to get to collide and that's 100 [cm]/(100/60)[cm/sec]. Simplifying I get 60 seconds.
    Maybe I've over complicated it a little bit :

  16. I don't understand…I mean, I get the idea, but I can't see how it works. Consider the last 4 ants on the stick, assuming they're facing alternating directions and the last ant faces toward the center of the stick. Now look at the 2nd ant: it moves 0.5cm, bounces off the end ant, which then proceeds to walk off the stick. Meanwhile, the 2nd ant walks back 0.5cm, bounced off the 3rd ant (which has just reached its starting point again), turns around, and walks 2cm off the end. (Cont'd below)

  17. That's a bit confusing… are you going on the assumption that the time it takes for an ant to turn around = the amount of time it takes for an ant to pass through another ant? 0:35 – 1:00

  18. if they are evenly spaced and each ant is in the middle of each cm would the shortest time not be when the ant walks 49.5cm which is 0.495 minutes and the longest time would be for the ant on the end to walk the longest way which is 99.5 cm which would take 0.995 minutes? Can somebody explain to me.

  19. If they collided they would turn around and you would still get the same result. 30 seconds the quickest and 60 seconds being the longest.

  20. Only if they had zero length or volume, and singing banana has already answered this by saying the ants are points. If the moving objects themselves have length then it does not equate. Extreme example being, say, oil tankers moving across a channel.

  21. You're exactly right. .495 minutes is 29.7 seconds (which he accepts as valid in the video) and .995 minutes is 59.7 seconds.
    You just didn't convert your units to the ones he asked for.

  22. Me too, when I first attempted this, I was calculating them bouncing back and forth for longer and longer distances exponentially, and got an answer something like 7000+ years, which wasn't at all right. When I tried it again I got a more reasonable answer, but I was still off.

  23. i was thinking of this diffidently and was thinking that you have a bunch of ants moving in one dimension on a tow dimensional surface they never needed to hit one another.

  24. It's like elastic collisions. The motion is equally transferred, so they are the same ball, essentially! beautiful. Also, it's not quite a minute, because of the fact that 100 ants spread across a meter equally with no width wouldn't be on the edges. The last and first and would be 1/2 a centimeter from the edge. with 101 ants, it would take a minute.

  25. you didnt say in the question where the ant was placed, you said "some ant heading left some ant heading right, what if the ant in the end is heading to fall off it would take 0.6sec to fall off right?? and the next ant would take 1.2sec. the fact is you didnt say where the ant was placed. so the shortest time must be 0.6 sec and the longest must be 1minute

  26. 29,7 is more accurate for the shortest time, because of the fact that the ants were evenly distributed. 
     There is an even number of Ants.
    30 seconds is from the center, but with an even number the center ants will not be exactly in the middle.
    The number of spaces in between ants is 99 (not 100)
    The space between ants is 100 cm / 99 = 1.01010101010101………cm
    The distance between the center and the 2 center ants will be half of the space between ants: 1.010101…/ 2 = 0.505050505……cm
    Meaning that the 2 center ants are 50-0.50505…= 49.49494949…..cm away from the nearest edge.
    And with 1meter per minute, the time would be 29.7 or 29.69696969696969…….. sec.

  27. what about an ant all the way at the right, walking right, would it not go off instantly, thus making 29.7 not the shortest time?

  28. I really liked this problem and honestly I didn't thought about this beautiful solution but I disagree on a point.
    In fact I think that the fist ones to fall will be the ants that were on the borders because it's like they are passing through each other but in reality they are colliding.
    So i think that as said in the video the first one will fall after 30 sec but it will be a border ant and the last ones will fall after a minute and they will be the ants that clashed for first.

  29. Ha, finally a problem I got correct, although my way of thinking was not nearly as elegant. The shortest time was easily determinable. Every ant walks towards its closest end of the cane, so 29.7 seconds until all of them have fallen off. The longest time was tricky. Every 0.5 seconds, ants meet each other and change directions. Through trial and error, you can work out that there will always be a point when every ant meets another ant (pairs of 2). No ant does not have a partner. This point is reached after "Number of ants / 2" steps when each step is 0,5cm. To resolve this, it equally takes "Number of ants / 2" steps of 0.5 cm until every ant walks towards the end of the cane. In total, it takes "Number of ant" steps of 0.5 cm until we reach the optimal starting point (each ant walks towards its nearest end of the cane) from the worst starting point (ants on the left-hand side of the cane face rightwards, ants on the right-hand side of the cane face left-wards). So the longest time is what it takes to cross 0,5cm*100+49.5cm, which is 59.7 seconds.

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