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 go well with and worth in 4 playing cards with out the posh of selecting these 4 playing cards arbitrarily from the entire deck.

The go well with is straightforward. In 5 playing cards there should be a double of no less than one go well with. So the primary (or final, however I’ll select arbitrarily) card within the bunch she passes is identical go well with as yours. Now there are three playing cards left to encode a quantity from 1 to 13. However Alice selected which card of your go well with to go to Bob and which to return to you. She can select in line with a rule that will get the variety of doable playing cards down considerably.

The three handed playing cards will be designated small medium and enormous in line with their quantity, after which breaking ties by go well with order (golf equipment smallest, diamonds, hearts, spades as in bridge.) This provides six doable 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 go well with playing cards to go and which to return? Bob will add the encoded quantity to the handed card (going round Ok-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 go 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 Ok she passes the Q and encodes 1. If you’ve the 7 and Ok she passes the 7 and encodes 6. But 6 and Ok, she passes the Ok and encodes 6.

I’ve tried to discover a set of playing cards you may select, understanding this algorithm, that might make it not possible to carry out the trick, and I can not. Not from a correct deck that does not have any duplicate playing cards.