Now again this one isn't a trivial problem. And you needn't be a mathematics geek to attempt it. One of my friends asked this to me. At first it looked like an olympiad problem which the leeser mortals like me dare not attempt, but later I found a rather simple solution for it. Let's see how you attempt it.
There are 8 ants. Each of the ants is moving at a constant velocity (meaning, at a constant speed in a straight line). Velocities may be different for all ants. The paths of no two ants are parallel. Now, it is given that two of these ants meet all other ants in their way. You have to prove that every ant meets every other ant in its way.
As simple as that.
Solution:
It will be very difficult (and impossible for dumb people like me) to solve it using equations and variables and stuff. When this guy first asked me this puzzle he claimed to have an elegant solution for it, but seemed quite convinced that I won't be able to crack it this time. Anyways, he had warned me against using equations and stuff to solve this.
So how did I first approach the problem? I used 'equations and stuff'! With a paper and pencil - for several minutes - till finally I conceded defeat. I could not solve the problem. When I went to bed, the ants were still moving in my head. One ant meeting all others . . . all ants meeting each other . . . 'elegant solution' . . . ants coming towards each other . . . elegant solution . . . ants coming towards each other relatively . . . and then suddenly one ant stopped. It stopped. All other ants started moving relative to this ant. This stationary ant was one of those who would meet all others. So all other ants would start moving towards this ant. At different speeds, but towards the same point - from all directions. It would make a star-like figure with the stationary ant at the centre. Now there is another ant which needs to meet all other ants . . . and there is only one way it could do that . . . Yes . . . now you got it. Eureka!!
My friend still maintains that he has an even more elegant solution. Let's see if you could help me with that.
For detailed solution, click here.
More discussion at The Time Dimension (A very innovative solution to the problem !)
There are 8 ants. Each of the ants is moving at a constant velocity (meaning, at a constant speed in a straight line). Velocities may be different for all ants. The paths of no two ants are parallel. Now, it is given that two of these ants meet all other ants in their way. You have to prove that every ant meets every other ant in its way.
As simple as that.
Solution:
It will be very difficult (and impossible for dumb people like me) to solve it using equations and variables and stuff. When this guy first asked me this puzzle he claimed to have an elegant solution for it, but seemed quite convinced that I won't be able to crack it this time. Anyways, he had warned me against using equations and stuff to solve this.
So how did I first approach the problem? I used 'equations and stuff'! With a paper and pencil - for several minutes - till finally I conceded defeat. I could not solve the problem. When I went to bed, the ants were still moving in my head. One ant meeting all others . . . all ants meeting each other . . . 'elegant solution' . . . ants coming towards each other . . . elegant solution . . . ants coming towards each other relatively . . . and then suddenly one ant stopped. It stopped. All other ants started moving relative to this ant. This stationary ant was one of those who would meet all others. So all other ants would start moving towards this ant. At different speeds, but towards the same point - from all directions. It would make a star-like figure with the stationary ant at the centre. Now there is another ant which needs to meet all other ants . . . and there is only one way it could do that . . . Yes . . . now you got it. Eureka!!
My friend still maintains that he has an even more elegant solution. Let's see if you could help me with that.
For detailed solution, click here.
More discussion at The Time Dimension (A very innovative solution to the problem !)
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