“Hidden Card” riddle
Posted by Rob Herman at July 11th, 2006
Today, a riddle.
I issue you and a partner the following challenge: I hand you five cards from an ordinary deck (no jokers). You stamp the numbers “1” “2” “3” and “4” on four of the cards, and hide the fifth. The choice of which to write on and which to hide is yours. You then leave the room and your partner enters. Given the four marked cards, your partner must guess the identity of the hidden card.
What strategy do you and your partner agree on beforehand that allows you to determine the hidden card? There is no need for trickery like imparting some meaning to the location of the mark on the card.
Warning: As it turns out, there is a lot of wiggle room in the solution. In fact, a solution exists even if the deck has 120 cards! Despite this, the riddle is strikingly hard. To my shame, I had to look up the answer, because after several hours, it was keeping me from getting any work done at the office. A mathematical background is not needed for the 52-card riddle, but it’s probably very useful if you try for 120.
Hint 0: A solution exists.
Hint 1: If you are like me, you will be tempted to throw away the ideas of suit and rank and just index the cards 0-51. While there is technically nothing wrong with this, starting with the cards divided into 4 groups is actually very natural and lends itself to an elegant solution.
Thanks to reader John Rhoadhouse for his help and thoughts in this and other riddles.
In other news: By popular demand, the return of 1KBWC next Sunday! If you are interested, let me know.
Curse my linear thinking. I was so close, but I have things to do today too. I am glad that I didn’t try the one with the larger deck though, the math required uses statistical terms I did not remember the meaning to. It is a bit cruel to post this without a link to the answer it took me a couple of minutes to google the answer.
I didn’t put the “linear thinking” hangup in the main article because I considered it too much of a hint, but that’s what hung me up too.
Putting a link to the solution would make it too easy. What I should do is put in a list of Google search terms that will be helpful. Try “hidden card riddle”.