[This is another one of those puzzles that seem impossible at first]
You live in a one dimensional world, where the unit of time is seconds and everyone is immortal. At time = 0 seconds, a magical monkey appeared at some integer co-ordinate, and is known to be moving at a constant integer speed.
If it was at position x at time $t$ seconds, then it disappears, and then reappears at some position $x + v$ ($v$ could be negative) at time $t+1$ seconds, where it stays for a brief moment, then disappears and reappears at $x+2v$ at $t+2$ seconds and so on.
Both the initial point of appearance, and the speed of the monkey are not known to you, and you have no record of where the monkey has been so far.
You have access to magic too, and can appear at any point of your choosing. If you appear at a certain point the same time as the monkey, you can catch him.
In your world, time progresses linearly, and there is no time travel etc.
Can you catch the monkey in a finite amount of time (assume the current time is some $T \gt 0$)? (i.e. catch him eventually, and not be on a chase forever).
[Solution]
You live in a one dimensional world, where the unit of time is seconds and everyone is immortal. At time = 0 seconds, a magical monkey appeared at some integer co-ordinate, and is known to be moving at a constant integer speed.
If it was at position x at time $t$ seconds, then it disappears, and then reappears at some position $x + v$ ($v$ could be negative) at time $t+1$ seconds, where it stays for a brief moment, then disappears and reappears at $x+2v$ at $t+2$ seconds and so on.
Both the initial point of appearance, and the speed of the monkey are not known to you, and you have no record of where the monkey has been so far.
You have access to magic too, and can appear at any point of your choosing. If you appear at a certain point the same time as the monkey, you can catch him.
In your world, time progresses linearly, and there is no time travel etc.
Can you catch the monkey in a finite amount of time (assume the current time is some $T \gt 0$)? (i.e. catch him eventually, and not be on a chase forever).
[Solution]
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