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Four snails travel in uniform, rectilinear motion on a very large plane surface. The directions of their paths are random, (but not parallel, i.e.any two snails can meet), but no more than two snail paths can cross at any one point. Five of the (4 X 3)/2 = 6 possible encounters have already occured. Can we state with certainity tha the sixth encounter will also occur?
Comments (5)
.. obviously now you know the answer.. why don't you try it once more?
Kaymant sir, I think I've finally got it....
We know 5 encounters have already occured, so any snail suppose be X has met 3 of his friends ----say P,Q,R.....
Now in my reference frame, X is at the origin....
P,Q,R thus have crossed the origin, For the remaining 2 encounters, P have met both Q & R.
Which further signifies that P,Q,R are moving in a st.line, thus the other 2.....Q&R must also meet each other at some other time.....thus 6 encounters is a must......
PLZ CORRECT & GIVE THE FULL SOLN IF I'M WRONG!
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Sir,
this is not a rigorous proof ---- just intuition.
Correct me if I'm wrong.