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Mind-Swapping Machine (Posted on 2012-08-02) Difficulty: 3 of 5
I am a mad scientist, and I have invented a machine that will switch the minds of two people into each other's bodies.

Being mad, though, my machine has one fatal drawback: once two bodies have used the machine, then the machine will never work again on that particular pair of bodies (regardless of whose minds are inhabiting them currently).

Here's an example. Bodies A and B use the machine, so person a is in Body B, and person b is in Body A.

Body   A B C
person b a c

Next, suppose Bodies A and C switch, so person c is in Body A, and person b is in Body C.

Body   A B C
person c a b

Finally, B and C switch, so person a is in body C, and person b is back in Body B.

Body   A B C
person c b a

Unfortunately, bodies A and C have already gone through the machine, so the machine will not work on that pair again. Therefore, if we want to restore everyone to his original body, at least one more additional body is needed for temporary storage.

Question 1:
At the beginning, once bodies A and B switch, can they ever switch back, leaving all others in their rightful bodies when all is said and done? If so, how many total bodies would need to be involved (including A and B)?

Question 2:
Suppose n people continue to switch bodies with other members of their group (again, each pair of bodies can only use the machine once). How many total bodies, in terms of n, would need to be involved to sort everyone out?

No Solution Yet Submitted by Dustin    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Part II clarification Comment 4 of 4 |
(In reply to Part II clarification by Steve Herman)

In part 2, there are n people.  They have gone through a number of switches up to n*(n-1)/2 (the maximum number of switches possible).

I had originally intended switches that "randomized" n people, but how does one determine how to do so?  Do you choose a random number between 1 and n*(n-1)/2 and then do that many switches?  Do you put all possible pairs of people in a hat, and continue to draw and switch until all possible switches have been done?

Instead, I think this would be fair:

A group of n people is presented to you, where each person has switched at least once with some other person in the group.

For example, 6 people may have done A/B, C/E, B/F, D/A.

Sorry about rambling in this post!

  Posted by Dustin on 2012-08-03 04:04:21
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