This was a difficult puzzle overall, and only two people sent correct answers – Aman Singla and Girish Tutakne. I think in the end this was a bit difficult for children!
I am reproducing the answer from Aman, Girish had sent a similar answer:
50 (the number Peter sent) reach Cynthia; 20 (the number Cynthia sent) reach Peter; 1000 collisions.
Since the number of ants headed in each direction is still the same following the collision, mathematically, one can assume that a collision is same as one ant climbing on top of the other and crossing over. So 50 will eventually reach Cynthia, and 20 Peter. And each of the 50 reaching Cynthia will have had to cross over 20 headed towards Peter – hence 1000 crossovers/collisions.
Hope you enjoyed the puzzle!