Can a monkey outrun a bullet and still save her litter?

[Evo]

Collinsmark explained your error.

 

[Jimmy Snyder]

Let's assume that the bullet is like a cartoon bullet. That is, it follows the path of the victim. This is different from the way a heat seaking missile would work. When the target makes a right turn, the heat seeking missile would immediately turn as well so that it was always pointed directly at the target. However, a cartoon bullet would continue in a straight path toward the point where the victim turned. Then it might make a right turn and follow the victim, or it might slow down to a halt, shade its eyes and look for the victim and then make the right turn. We will assume that our cartoon bullets don't do that, but just follow the path of the victim. Let's also assume that the bullet will always chase after the mother, not the offspring.

Let's say that it takes x minutes to throw a litter and that the monkey has a lead time of y minutes before the bullet strikes. The monkey that runs faster than the bullet can throw her litter and survive since she can always run until y becomes greater than x. Once that happens, she can stop, throw her litter, get up and start running again and never get caught.

The monkey that runs as fast as the bullet never needs to be killed by it. However, if x is greater than y, she can never throw her litter as she will die before she finishes. Perhaps some offspring will survive, but not necessarily all of them. However, if x is less than y, then there is no problem. She stops, throws her litter, gets up and starts running again and never gets caught.

The monkey that runs slower than the bullet is in a similar situation as the monkey that runs as fast as the bullet. If x is greater than y, she cannot be sure of delivering her litter, but if x is less than y she can. The difference is that no matter whether she delivers or not, she will be killed by the bullet.

The problem is ill posed since we are not told whether x is greater than y. What's worse, if we are told, then the problem is trivial.