Thinking it over and over again, I always finish with a problem I cannot solve.
The holes are numbered 1, 2, 3....
Three hunters check:
1 2 3
3 4 5
5 6 7
....
On day n, they will have checked up to the hole 2 * n +1
The groundhog starts in the hole k and moves to the right.
On day n, he will be in the hole k+n
Question 1: Will the hunters catch the groundhog (and if so, when)?
2 * n +1 grows faster than k + 1, I already have the answer. Nevertheless:
2 * n + 1 = k + n
n ⁼ k + 1 No matter how high the number of the starting hole the groundhog choses, it will be caught.
Question 2: Is there a starting hole so that the groundhog is not discovered on day n?
k + n > 2 * n + 1
k > n + 1 No matter how long the hunters hunt, it always is possible that the groundhog started in a hole leading him outside the checked area.