[wolfgang]

Hi...cut 10 pieces of paper,write the numbers(1 to 5) on the first five papers.

then write the letters(A,B,C,D,and E)on the other five papers.

put the papers with numbers to your left side and the papers with letters to the right side.like this:

1..2..3..4..5--------------------A..B..C..D..E

your goal is to change their places at the same order,to make them like this:

A..B..C..D..E--------------------1..2..3..4..5

you should follow these roles:

1- you should always move two adjacent items together,e.g. two numbers,two letters,or a mixture.

2-the two selected items from each side should replace each other( this will be concidered as one move).

for example:if you choose(12) from the left side,and (AB)from the right side,so they should replace each other like this: A..B..3..4..5-------------1..2..C..D..E

3-you can choose any two adjacent items(e.g.for 3 you can choose either 23,or 34,but for 5, there is only 45).

4-you are not allowed to change the sequence of the pair,,i.e.(12) can not be (21).

Have a nice time...and we will see who can solve it with minimum moves.

[Smith]

Request for clarification...

Rule 2 states, in part, "the two selected items FROM EACH SIDE..." (emphasis mine). Does this preclude a move such as this:

Starting with

1..2..3..4..5 ----- A..B..C..D..E

select 1 and 2, 4 and 5 to get

4..5..3..1..2 ----- A..B..C..D..E

Or is that not legal because 1, 2, 4, and 5 are on "the same side"?

[Guest]

Another clarification question:

If you pick the first and second items on the left to move, does that mean you have to move the first and second items on the right? Or can you choose two others to move?

For example, can the first move be to switch 1 2 and C D to get C D 3 4 5 A B 1 2 E?

[Guest]

Hi...cut 10 pieces of paper,write the numbers(1 to 5) on the first five papers.

then write the letters(A,B,C,D,and E)on the other five papers.

put the papers with numbers to your left side and the papers with letters to the right side.like this:

1..2..3..4..5--------------------A..B..C..D..E

your goal is to change their places at the same order,to make them like this:

A..B..C..D..E--------------------1..2..3..4..5

you should follow these roles:

1- you should always move two adjacent items together,e.g. two numbers,two letters,or a mixture.

2-the two selected items from each side should replace each other( this will be concidered as one move).

for example:if you choose(12) from the left side,and (AB)from the right side,so they should replace each other like this: A..B..3..4..5-------------1..2..C..D..E

3-you can choose any two adjacent items(e.g.for 3 you can choose either 23,or 34,but for 5, there is only 45).

4-you are not allowed to change the sequence of the pair,,i.e.(12) can not be (21).

Have a nice time...and we will see who can solve it with minimum moves.

It can not be done.

Supposing we had a solution. We need only consider how to move the Letters as by symmetry the Numbers will get moved too. This means that each of the five letters had to be moved an odd number of times. (If a piece is moved an even number of times, it is returned to its starting pocket.) So the total number of piece moves must also be an odd number (five summed odds = an odd). But rules require us to move pieces in pairs. So the total number of piece moves must be an even number (if we play by the rules). This is contradiction--so the puzzle can not be completed as stated by the rules. Thx!

[superprismatic]

It's impossible to do. You are asking us to compose

a bunch of even permutations to make an odd permutation.

But, the composition of even permutations is always

even.

[Guest]

This does not swap all the letter correctly, but it does get all the letters and numbers swapped

12345 ABCDE (swap 12 with BC)

BC345 A12DE (swap 45 and DE)

BC3DE A1245 (swap C3 and 12)

B12DE AC345 (swap 12 and AC)

BACDE 12345

The letters are wrong, but the numbers are correct)

Edited May 20, 2011 by kevink

[wolfgang]

Request for clarification...

Rule 2 states, in part, "the two selected items FROM EACH SIDE..." (emphasis mine). Does this preclude a move such as this:

Starting with

1..2..3..4..5 ----- A..B..C..D..E

select 1 and 2, 4 and 5 to get

4..5..3..1..2 ----- A..B..C..D..E

Or is that not legal because 1, 2, 4, and 5 are on "the same side"?

Thank you....yes that is legal...you can switch between any two pairs.

[wolfgang]

Another clarification question:

If you pick the first and second items on the left to move, does that mean you have to move the first and second items on the right? Or can you choose two others to move?

For example, can the first move be to switch 1 2 and C D to get C D 3 4 5 A B 1 2 E?

No...you can choose any two items.

[wolfgang]

This does not swap all the letter correctly, but it does get all the letters and numbers swapped

12345 ABCDE (swap 12 with BC)

BC345 A12DE (swap 45 and DE)

BC3DE A1245 (swap C3 and 12)

B12DE AC345 (swap 12 and AC)

BACDE 12345

The letters are wrong, but the numbers are correct)

nice try...

[wolfgang]

Hi...cut 10 pieces of paper,write the numbers(1 to 5) on the first five papers.

then write the letters(A,B,C,D,and E)on the other five papers.

put the papers with numbers to your left side and the papers with letters to the right side.like this:

1..2..3..4..5--------------------A..B..C..D..E

your goal is to change their places at the same order,to make them like this:

A..B..C..D..E--------------------1..2..3..4..5

you should follow these roles:

1- you should always move two adjacent items together,e.g. two numbers,two letters,or a mixture.

2-the two selected items from each side should replace each other( this will be concidered as one move).

for example:if you choose(12) from the left side,and (AB)from the right side,so they should replace each other like this: A..B..3..4..5-------------1..2..C..D..E

3-you can choose any two adjacent items(e.g.for 3 you can choose either 23,or 34,but for 5, there is only 45).

4-you are not allowed to change the sequence of the pair,,i.e.(12) can not be (21).

Have a nice time...and we will see who can solve it with minimum moves.

Is it so difficult!!!

O.K....here is a small hint....try to rearrenge the right side so that it will be like this:

1..2..3..4..5------------------B..A..C..D..E

I am sure you can do it!!

[Guest]

I was able to get it to be 12345 and bacde and then switch the sides so abcde is on left and in order, but that process put the numbers out of order and they can not go back in order without doing some switching with the letters side, which then puts the letters out of order and they can't get right without putting the numbers out of order, etc. If there is a solution, it requires a grasp of the puzzle dynamics that eludes me.

[k-man]

I was able to get it to be 12345 and bacde and then switch the sides so abcde is on left and in order, but that process put the numbers out of order and they can not go back in order without doing some switching with the letters side, which then puts the letters out of order and they can't get right without putting the numbers out of order, etc. If there is a solution, it requires a grasp of the puzzle dynamics that eludes me.

It's impossible to reach 12345...BACDE from 12345...ABCDE by following the rules as others have already mentioned. You must have made a mistake somewhere along the way. Getting from 12345...BACDE to ABCDE...12345 is pretty straight forward. Just follow the steps in kevink's post.

[Guest]

It's impossible to reach 12345...BACDE from 12345...ABCDE by following the rules as others have already mentioned. You must have made a mistake somewhere along the way. Getting from 12345...BACDE to ABCDE...12345 is pretty straight forward. Just follow the steps in kevink's post.

Right, I was working the problem forward and backwards and missated what I had found. I never had 12345 and bacde at the same time, it was 23541 and bacde. Oops.

[Guest]

12345 ABCDE

{12} <=> {AB}

AB345 12CDE

{34} <=> {DE}

ABDE5 12C34

{DE} <=> {C3}

ABC35 12DE4

{35} <=> {DE}

ABCDE 12354

Edited May 27, 2011 by Dej Mar

[wolfgang]

Sorry....I did a mistake....there is no possible solution according to these roles ,,,thus Kevink`s post was the best solution...