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Interview Puzzle- "Fox in a hole"

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The second half of the solution seems to be inefficient though.  Once we stop at hole 4 and conclude that the fox is in fact at an even hole the only hole left is hole number 2 which means that we don't need to start all over.  Simply inspecting three and then two would be enough to find the fox.

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Six-step solution:

Spoiler

Check holes in this order: 2, 3, 4, 2, 3, 4. After one of these steps the fox is found.

Why this works:

Spoiler

Assume fox's initial hole is even.

(1) 2: found, or in hole 4 and moves to 3 or 5.
(2) 3: found, or in hole 5 and moves to 4.
(3) 4: found, or it was case 2 and fox's hole
now is even. Repeat steps 1-3.

 

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Don't watch the video!!!

it is a good video, it clearly states the problem, but then it gives the answer! (Clearly stated as well)

if you watch the video, stop after the problem statement. 

I enjoy the problem, and I appreciated the ingenious solution, nice job!

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9 hours ago, BMAD said:

The second half of the solution seems to be inefficient though.  Once we stop at hole 4 and conclude that the fox is in fact at an even hole the only hole left is hole number 2 which means that we don't need to start all over.  Simply inspecting three and then two would be enough to find the fox.

Exception which means it could be 4

check hole 2 fox is in  5

check hole 3 fox is in 4

check hole 4 fox is in 3

check hole 2 fox is back in 4

 

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18 hours ago, bonanova said:

I agree with BMAD's 5-step solution. I missed it.

No, BMAD's 5-step solution is incorrect for the reason that CaptainEd brought up.

On July 19, 2017 at 3:14 AM, BMAD said:

Once we stop at hole 4 and conclude that the fox is in fact at an even hole the only hole left is hole number 2 which means that we don't need to start all over.  Simply inspecting three and then two would be enough to find the fox.

Hole 4 hasn't been eliminated for Day 4, only for Day 3. On Day 4, it could still be in either hole 2 or 4.

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