I’m going to imagine Alice regarded on the playing cards and selected which one to present again to you. The key to the puzzle is then to encode a single card’s swimsuit and worth in 4 playing cards with out the luxurious of selecting these 4 playing cards arbitrarily from the entire deck.

The swimsuit is straightforward. In 5 playing cards there should be a double of at the very least one swimsuit. So the primary (or final, however I’ll select arbitrarily) card within the bunch she passes is identical swimsuit as yours. Now there are three playing cards left to encode a quantity from 1 to 13. However Alice selected which card of your swimsuit to move to Bob and which to return to you. She can select based on a rule that will get the variety of attainable playing cards down considerably.

The three handed playing cards could be designated small medium and huge based on their quantity, after which breaking ties by swimsuit order (golf equipment smallest, diamonds, hearts, spades as in bridge.) This offers six attainable numbers to be represented by the three handed playing cards based mostly on their order: SML, SLM, MLS, MSL, LSM, LMS.

So how does she select which of the swimsuit playing cards to move and which to return? Bob will add the encoded quantity to the handed card (going round Okay-A-2 if want be) to get the returned card. Alice passes whichever card is inside an add of 6.

Say you’ve the two and 4 of spades in your 5. She cannot move the 4 as a result of no quantity between 1 and 6, added to 4, will wrap round to the two. So she passes the two and encodes 2 within the different three playing cards by ordering them SLM. If you’ve the Q and Okay she passes the Q and encodes 1. If you’ve the 7 and Okay she passes the 7 and encodes 6. But 6 and Okay, she passes the Okay and encodes 6.

I’ve tried to discover a set of playing cards you would select, realizing this algorithm, that will make it unattainable to carry out the trick, and I am unable to. Not from a correct deck that does not have any duplicate playing cards.