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#1 nikolas

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Posted 26 February 2014 - 08:09 AM

Hello everyone,

i recently encountered a logic problem which is this:

There is a list(original) that contains all numbers from 1...n, without duplicates and not necessary in order. We dont know that list but we know

5 other lists which are the result of the original in that way: The first list came from moving one number from the original list to another position( be careful, move not exchange),

the second list came from moving another different number from the original list. What actions you must do to find the original list?

for example: 5 lists={[1,2,5,3,4],[1,5,3,4,2],[4,2,1,5,3],[2,3,1,5,4],[2,1,3,4,5]} and the original is Original=[2,1,5,3,4].

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#2 bonanova

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Posted 26 February 2014 - 11:17 AM

Spoiler for First thoughts

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#3 fabpig

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Posted 26 February 2014 - 02:39 PM

I'm assuming that the number of lists given is always n?

Superb puzzle, nikolas

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#4 nikolas

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Posted 26 February 2014 - 02:45 PM

@fabpig the numer of elements each list contains is n(variable). In this case n=5, and n>=3 always because of the number of permutations. e.g. for n=2, n!=1*2=2<5, but 3!=1*2*3=6>5 and as a result we can have the 5 lists.

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#5 nikolas

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Posted 26 February 2014 - 03:15 PM

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#6 fabpig

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Posted 26 February 2014 - 04:39 PM

@fabpig the numer of elements each list contains is n(variable). In this case n=5, and n>=3 always because of the number of permutations. e.g. for n=2, n!=1*2=2<5, but 3!=1*2*3=6>5 and as a result we can have the 5 lists.

Not sure if that's what I'm asking .  If there are eg. 9 elements, will there be 9 lists (that way, we know that each element has been moved once)?

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#7 nikolas

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Posted 26 February 2014 - 05:00 PM

@fabpig Ohh i see, no there will be only 5 lists!

Hint: its 5 lists and only no matter how many elements you have, number 5 plays a role!

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#8 fabpig

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Posted 26 February 2014 - 08:20 PM

Spoiler for OK..let's see if this makes sense, just for starters...

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Posted 26 February 2014 - 09:54 PM

for example: 5 lists={[1,2,5,3,4],[1,5,3,4,2],[4,2,1,5,3],[2,3,1,5,4],[2,1,3,4,5]} and the original is Original=[2,1,5,3,4].

I understand that to go from [1,2,5,3,4] to [1,5,3,4,2] can be easily achieved by moving the 2 to the rear but how does one then go to [4,2,1,5,3]? Can we slide two numbers at once?
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Posted 26 February 2014 - 09:57 PM

also, is it that we can't move the same number consecutively or is it that we can't do the same number more than once?
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