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The Magic Cafe Forum Index » » Magical equations » » Rusduck Challenge 100 percent solved - Purloined (0 Likes) Printer Friendly Version

glowball
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Rusduck challenge 100% solved

Rusduck put out a challenge for magicians to come up with a way for 4 randomly picked cards to be arranged face up so that his assistant could look at those four cards and determine a fifth randomly chosen target card that was set aside out of view. No external signals allowed, no forces, just the four cards used as a signaling means.

Note that I have posted similar solutions that did not quite meet the Rusduck criteria:
1. "Four Sevens" lets the spectator pick the target card but the magician selected the 4 signal cards ie the 4 sevens.
2. "Three Eights" lets the spectator pick the target card but the magician selected the 3 signal cards ie the 3 eights.
3. "Rusduck 90 percent solution" has the spectator pick the signal cards and pick the target card but 5 to 10 percent (depending on which variation) of the time it needs an "out" because it uses a limited number of one-way signal cards (one-way on the faces).

Others have come up with clever solutions that involve external signals or involve turning one or more of the four signal cards face down (I really like Colm Mulcahy's paper and Derrick Chung's use of binary for the high cards) which almost meets the Rusduck criteria.

My below 100 percent solution I'm going to call "Larfin's Purloined" as a play on words because the secret Purloined Letter was right in front of everybody's face.

If you buy a brick of bicycle cards (I think there is 13 decks) and look through each deck there is a good chance that you'll find one or two decks where the printing is off a little bit vertically.

Look at the white space just above the indices and it may be considerably more than the diagonally opposite indicie white space.

Sometimes if you have two slightly misprinted decks you can go through card by card (of course the backs must be the same color) and compare which card from which deck makes the better one-way card. I have done so and have two such decks that are easy to tell on every card which way is up.

You really don't want cards that are so grossly off center that they stick out like a sore thumb to the audience, instead just a little bit off center vertically so that your assistant can tell but nobody else will notice.

The specifics of my 100 percent solution are (using SHoCkeD for any tiebreakers). Note that these are the same first four steps as my 90 percent solution but step five and on is different:

The magician arranges the four cards as follows:
1. holds the four cards in a fan facing himself
2. temporarily moves the highest card to the far right of the fan so he can easily focus on the other three cards.
3. uses the other three cards to indicate a value of 1-6 ie LMH is 1, LHM is 2, MLH is 3 etc. Note that if the spectator set aside target card is greater than six then the magician mentally subtracts six from that target card to arrive at the 1-6 value. If the set aside target card is a king just treat it as though it's a queen ie indicate six.
4. to indicate the target card suit: now position the highest card (that was temporarily moved to the far right of the four card fan) using the Stewart James principle to insert that card amongst the other three cards in the appropriate SHCD position.
5. If the target card is ace through six look at the card in the far left position of your four card fan and make sure you have the small amount of white space oriented up. If the target card is a seven through king then make the large amount of white space be oriented up on the far left card in the 4 card fan.
6. now to differentiate between a queen and a king: look at the second card (from the left) in the fan and orient the card to make the small white space at the top for a queen but orient that second card so there is a large amount of white space at the top for a king.
7. the third and fourth card's white space is not needed for this 100% solution however they could be used to signal more info such as which pocket the target card is in (third card white space indicates spectator's left or right pocket). The fourth card white space could be used as a base so that the first and second cards' white space could be interpreted as relative to the fourth card's white space (this would protect against the spectator rotating the entire packet vertically 180 degrees).

That's it, but this packet must be consistently held vertically the correct way by the spectator when delivering it to the magician's assistant (unless the fourth card's white space is utilized as a reference to the other cards' white space then the assistant will interpret the earlier cards' white space correctly regardless).

What the assistant does after receiving the packet:
1. makes sure that the packet is correctly held vertically so that it is not upside down and fans the four cards facing himself.
2. looks for the highest card (uses SHCD for any tie breaking) and determines the suit based on the relative position of that card (SHCD) and mentally repeats the suit name a few times to cement the suit name into his brain and then jogs that card down halfway to get it out of view while he evaluates the other three cards:
3. evaluates the other three cards LMH etc to come up with the 1-6 value.
4. next looking at the leftmost card in his 4 card fan If there is big white space above the left top indicie he adds six to the 1-6 value.
5. If the value is 12: the magician's assistant looks at the second card from his left and if there is big white space above it's left top indicie then the target card is a king otherwise the target card is a queen.
6. optional: The magician's assistant looks at the third card from the left and if the white space is small then the target card is in the spectator's left pocket otherwise if the white space is large the target card is in the right pocket.
7. optional: steps four and five can be evaluated versus the fourth card's orientation. Example: in determining whether to add six to the 1-6 value, instead of mentally determining whether the leftmost card's white space is at the top mentally ask does the white space at the top of the first card match the white space at the top of the fourth card and if so then add six. Use the same approach for the second card's white space and the third card's white space (If doing the left right pocket bit).

Note that there are no outs necessary and no equivocates, this works 100% of the time (provided the magician and his assistant don't goof up).

This approach can be used with any deck that has one way faces such as Phoenix decks that hcs has mentioned in my Rusduck 90 percent solution thread.

Note that when looking for slightly off centered vertically faces that we really want the backs to be nearly perfectly centered so as to not call attention to the cards.

Like the term "Purloined" because I like to use the theme of catching a thief (the target card) via four detectives (the four signal cards).
Francois Lagrange
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I can’t see your solution being an improvement on the Cheney method which is 100% math and generic. With the latter any borrowed deck of cards can be used, in yours it has to be your own made-up deck. You might as well use any of the special decks sold in magic shops or use the 18th century old-style playing cards which have only one index.

But if you’re happy, fine of course.
Protect me from my friends, I'll deal with my enemies.
glowball
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The Cheney method the spectator does not get to pick which one of the five is the target card. I believe this was Rusduck's criteria major complaint with the Cheney method. By combining the 1-6 LMH method with one-way faces this overcomes that complaint. Still, Cheney is my hero.

This has been more of an academic challenge to solve the Rusduck criteria than a trick that I will actually perform very much. It ain't the greatest trick in the world. And you have to have a trained assistant with you to do this trick.

I agree that normally the magician must use his own deck when using my method but my guess is the vast majority of the time the Fitch Cheney trick is done with the magician's deck.

I just now opened a fresh deck of regular old bicycles and bingo all the cards have one-way faces (printed vertically off center a little bit). These decks may be more prevalent than we realize because card manufacturers are more concerned with the backs of playing cards being asymmetrical ie gambler Phil Ivey edge reading. The faces of playing cards being asymmetrical is not nearly as big a concern to them.
glowball
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Some decks will have vertically centered faces but will be horizontally off a little bit. These decks are one-way because the white space to the left of the indicie and left of the little pip will be greater than the white space of the diagonally opposite indicie and little pip.

It's the exact same principle as utilizing the white space above the indicie.
glowball
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This video is interesting about Phil Ivey and Cheung Yin Sun using the asymmetrical imperfections on casino cards. They won over $20 million but the courts have ruled they had to give the money back.

https://youtu.be/k52cGJrehec

If anybody wanted perfect decks the casinos should be the best, but yet this happened.

So apparently there is no such thing as a perfect deck it's just a matter of degree and whether our eyes can detect the imperfection.
glowball
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See the following 2 threads about one-way facers which are also called pointer cards. All the posts appear to be about the magician performing by himself to find a selected card that has been reversed or similar such effects.

I didn't see any posts that used the one-way principle to encode a selected card similar to the Fitch Cheney trick. However there are some interesting posts in these two threads such as the fact that older bicycle spade face cards (JS, QS, KS) had a hard to detect one-way design.

https://themagiccafe.com/forums/viewtopi......orum=201

https://themagiccafe.com/forums/viewtopi......orum=37a
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