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There are five holes in the ground that a certain groundhog likes to hang out in. These holes are in a row. You are allowed to look in one of the holes at noon each day. Every night, while you aren't around, the groundhog will leave the hole he is in, and move to an adjacent hole. For example, if he's in hole #2, he can move to hole #1 or #3. If he's in hole #1, he can only move to hole #2. What search strategy can you use, to ensure that you will eventually find the groundhog? Using the most efficient strategy, what is the maximum number of days it could take you to find him?

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I pick holes in these order.

3 (gotta start somewhere) 1/5 chance of catching him

2 (moving aside, i caught him if he started at 1) 1/5 of catching him

2 (same spot, if he started at 2, and moved to 1, he'd have to move to 2. 1/5 chance of catching him at this point.

i cant figure out any more how to check the last to spots (or the third spot by now for that matter)

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depending on the intended definition of "find him" either meaning know which hole it is in or looking in the hole with the groundhog, would say either 4 or 6 days. Day 1 look in a hole one from the end (let's say hole #2 in this case). Day 2 and 3 look in the other hole one from the end (hole #4). So after the third day if you have not found it, you know it must be in either hole #1 or #3. Day 4 look in hole #2 and if it's not there you know it's in hole #4. Day 5 look in hole #3. If not there then day 6 it will be in hole #4.

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Day 1, choose hole 2: gopher can be in 1, 3, 4, 5

Day 2, choose hole 3: gopher can be in 2, 4, 5

Day 3, choose hole 4: gopher can be in 1, 3

Day 4, choose hole 4: gopher can be in 2

Day 5, choose hole 3: gopher can be in 1

Day 6, choose hole 2: gopher must be there!

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Below is the solution for finding the groundhog. It can be done in 11 days.

S1 to S4 are the possible starting points of the groundhog and 1 deenotes which hole to look into on a particular day.

post-17784-12756611416101.jpg

Edited by DeeGee
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7 days. The 6 day theories had holes, see the logic below

2 1345

2 345 if 5, then 4 if 4, then 3 or 5 if 3, then 4

4 235 if 3, then 2 if 4, then 3 or 5

4 135 if 2, then 1 or 3 if 3 then 5

4 2 if 1 then 2 if 3 then 2

3 1 if 2, then 1

2 caught

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7 days. The 6 day theories had holes, see the logic below

2 1345

2 345 if 5, then 4 if 4, then 3 or 5 if 3, then 4

4 235 if 3, then 2 if 4, then 3 or 5

4 135 if 2, then 1 or 3 if 3 then 5

4 2 if 1 then 2 if 3 then 2

3 1 if 2, then 1

2 caught

4 135 if 2, then 1 or 3 if 3 then 5

I don't understand this statement, shouldn't it be if 3 then 2?

Which would make the next statement incorrect. Or am I not following you?

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assuming that the groundhog may move to holes he's already been in, and in order to find the maximum number of tries you must assume he happens to continually move awa from your next peek.

step1. hole 2

step2. hole 1

step 3. hole 2

step 4. hole 3

step 5. hole 4

we know he muct be in hole 5

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Most Systematic]I would start at one end or the other and work my way one hole at a time therefore if I started at hole one and followed that by hole two the next day, I could get lucky and catch him early, but when i look in the fourth hole on the fourth day, and he is not in there then he is in the fifth hole. It would take no longer than four days. Unless the little bugger runs.

Edited by mkohus
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I would start at one end or the other and work my way one hole at a time therefore if I started at hole one and followed that by hole two the next day, I could get lucky and catch him early, but when i look in the fourth hole on the fourth day, and he is not in there then he is in the fifth hole. It would take no longer than four days. Unless the little bugger runs.

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let me better explain my logic...

step1. peek in hole 2 (not there)

step2. peek in hole 1 (we now know he did not move from 2 to 1)

step 3. peek in hole 2 (not there, could have moved to 3,4 or 5)

step 4. peek in hole 3 (not there, could have moved to 4 or 5)

step 5. peek in hole 4 (not there, must have moved to hole 5)

we know he muct be in hole 5

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@zooball,

The poster below you is correct, the groundhog can avoid you by going 5 4 3 2 1 2 3

@dudeguyinc

I'm seeing a hole (no pun intended) if the groundhog just goes 1 2 1 2 1 2

Here is my solution

2 2 3 3 3 4 4 3 2

See attached for a visual.

If I'm correct, 9 days is as fast as I'm able to get it.

post-25074-12756725269945.png

Edited by Namelessone25
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@zooball,

The poster below you is correct, the groundhog can avoid you by going 5 4 3 2 1 2 3

@dudeguyinc

I'm seeing a hole (no pun intended) if the groundhog just goes 1 2 1 2 1 2

Here is my solution

2 2 3 3 3 4 4 3 2

See HERE for a visual

If I'm correct, 9 days is as fast as I'm able to get it.

*takes off hat and bows*

I was just about to post that this is impossible because you can't block him if you can only place 1 block on each row, but you seem to have nailed it...

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whatcha, I think it would take 5 nights because if you start at hole 1, go to hole 2, then 3, then 4, then finally 5 you should cross over him at some point

Not quite true, for example

Where you look: 1 2 3 4 5

Where he is : 2 1 2 1 2

You'll notice that since he is able to move before you get to look in another hole, if the groundhog just switches back and forth between 2 and 1 you wont find him using a sweep.

I noticed in my previous post's picture, the "333" part was redundant, so I've just changed it to a single 3.

So here is my final answer:

2 2 3 4 4 3 2

You would then find him in only 7 days. Again, that's assuming my first post doesn't have any flaws :P

Edited by Namelessone25
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Zathros's 6 day solution in post #7 is one of four

optimal solutions. All possible groundhog moves

are covered by his solution. Plainglazed got it

first but I didn't spot it before editing this post.

2,3,4,2,3,4

2,3,4,4,3,2

4,3,2,2,3,4

4,3,2,4,3,2

Edited by superprismatic
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