# Thread: Think Of A Card

1. ## Think Of A Card

A card-shuffling machine always rearranges cards in the same way relative to the original order of the cards. All of the hearts, arranged in order from ace to king, were put into the machine. The cards were shuffled and then put into the machine again.

After this second shuffling, the cards were in the following order:

10, 9, Q, 8, K, 3, 4, A, 5, J, 6, 2, 7.

What order were the cards in after the first shuffle?

2. ## Re: Think Of A Card

Perhaps a clue is in order: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Assume the ace was in the second slot after the first shuffle.</span hide>

3. ## Re: Think Of A Card

Thanks for the clue, how about <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">9, A, 4, Q, J, 7, 3, 2, 10, 5, K, 8, 6</span hide> for a solution.

StuartR

4. ## Re: Think Of A Card

Well done, Stuart. This wasn't easy, as testified by the number of attempts. Perhaps this type of puzzle has little appeal to the regulars. Methinks I must keep them simpler. Or perhaps not!

5. ## Re: Think Of A Card

This was easy with the clue, but I had no idea how to approach it without.

Thanks

StuartR

6. ## Re: Think Of A Card

I'm thinking that without the clue this isn't a unique answer. Try putting together an answer when the A goes to the third slot instead of the second. Ok, well that didn't seem to work. Maybe the general solution is to assume the A is in spot 2, try it. It if works, fine - if not, the assume the A is in slot 3, etc, etc.

7. ## Re: Think Of A Card

You're right, starting with the A in any other slot leads rapidly to a contradiction.

StuartR

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