1. Now the groundhog can leave holes 1 and 5 going away from the other holes, realize there is no hole there, and run back to the hole he was in. Now that he can stay in 1 or 5, what would be the maximum number of days that it could take to find the groundhog using the most efficient strategy? If there is no strategy that will be sure to find the groundhog in a finite number of days, prove it. (Too easy?)

2. Now there are 12 holes arranged like the numbers on an analog clock. The groundhog must move to a neighboring hole every night, like usual. You realize there is no strategy that guarantees finding the groundhog in finite time, so you hire another person to check a hole once every day. What would be the maximum number of days before finding the groundhog using the most efficient strategy?

3. Same as 2, but with 3 people checking holes.

4. You have a 5 by 5 grid of holes, and the groundhog can move in the four cardinal directions. What is the minimum number of people needed before you can be sure to find the groundhog in a finite amount of time? How long does it take with that number of people?

(yeah, I tend to put multiple problems in threads... it's like a shotgun approach, hopefully 1 or 2 are really good.)

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## EventHorizon 15

1. Now the groundhog can leave holes 1 and 5 going away from the other holes, realize there is no hole there, and run back to the hole he was in. Now that he can stay in 1 or 5, what would be the maximum number of days that it could take to find the groundhog using the most efficient strategy? If there is no strategy that will be sure to find the groundhog in a finite number of days, prove it. (Too easy?)

2. Now there are 12 holes arranged like the numbers on an analog clock. The groundhog must move to a neighboring hole every night, like usual. You realize there is no strategy that guarantees finding the groundhog in finite time, so you hire another person to check a hole once every day. What would be the maximum number of days before finding the groundhog using the most efficient strategy?

3. Same as 2, but with 3 people checking holes.

4. You have a 5 by 5 grid of holes, and the groundhog can move in the four cardinal directions. What is the minimum number of people needed before you can be sure to find the groundhog in a finite amount of time? How long does it take with that number of people?

(yeah, I tend to put multiple problems in threads... it's like a shotgun approach, hopefully 1 or 2 are really good.)

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