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MathNet 2012 Question 38

Math Olympiad Vault · MathNet 2012

Question 38

A Magician lays out 36 cards in a $6\times6$ square (6 columns of 6 cards). A Spectator mentally selects a card and remembers its column. The Magician collects the cards in a suitable order and lays them out again in a $6\times6$ square. The Spectator then reports the column containing the selected card on each occasion. How can the Magician always identify the card? (L. Emelyanov)

The Russian version repeats the same trick and asks for a guaranteed procedure.