Lorayne's To-And-Fro Magic Square

Discuss the tricks and sleights which appear in Genii.

Postby Guest » 05/07/06 09:14 PM

Lorayne's To-And-Fro magic square reminded me of a little puzzle that people find VERY tough to solve, yet with a little trick you can solve it very quickly. It's an impressive mental feat.

It's related to the magic square in this trick, but with an additional level of toughness.

Rather than a "magic square" theme, it's a card puzzle that is an interesting mental demonstration.

You can also make a tie to the Sudoku puzzles which are currently the rage.

I'll describe the puzzle here, and in a follow up post give tips on the method. Don't read the next post until you've tried it without any help - to get a good understanding of how tough this is to laymen.

Take out the all four of the Aces, Kings, Queens, and Jacks. Shuffle them, and deal in a 4 by 4 square.

You solve the puzzle by switching pairs of cards so that each row and each column contain an ace, king, queen, and jack, as well as one of each of the 4 suits.

Have at it.


Sam
Guest
 

Postby Guest » 05/07/06 09:28 PM

Here's some comments, and the method.

It's actually possible to also make the diagonals, inner 4 cards, and outer 4 corners meet the same criteria (1 of each rank, and 1 of each suit). DO NOT POINT THIS OUT - it's actually how you solve the puzzle quickly!

Here's how to solve it quickly:

(1) Deal out the cards into a random 4 by 4 grid.
(2) Look at the innermost 4 cards. With 3 pair switches or less, you can "set them" (1 of each rank and suit). Once set, never touch them again.
(3) Swap cards as needed so that the main diagonals are set. Again - once set, leave them alone.
(4) Only 8 cards need to be set - the inner cards on each side. They will be uniquely determined by looking at the inner 4 and outer corners. (If you ever get "stuck" at this stage with an impossible condition, simply switch 2 of the inner 4 on a diagonal).

With practice, you can swap cards extremely quickly. Spectators have no idea what you are looking at, and what you are doing.

Give it a try. I've done this for many folks at my local cardroom, and they all love the puzzle, and are amazed:
(1) That it can be solved
(2) That it can be solved so quickly by you!


Sam

(4)
Guest
 

Postby Guest » 05/08/06 09:57 PM

You can also do the "To-And-Fro Magic Square " as demonstration with number cards.

If you ask the spectator to name any random four cards like 2, 3, 9, 4, then you hand him those cards and tell him to arrange them in any order, while you're removing the other 12 matching cards, and you can arrange them in Magic Square style really fast:

4-9-3-2
2-3-9-4
9-4-2-3
3-2-4-9

I did it this way just to practice, since I was in Starbucks with a pack of cards, and no paper and pencil.
Guest
 


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