h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Or the "21 card trick" or whatever it's called. This one is very easy, the trick performs itself more or less. Take 21 cards and lay them out on a table in three columns. Ask someone to pick a card (without saying which one, of course) and indicate which column it's in. Gather up the cards column by column, making sure to sandwich the indicated column between the other two. Lay the cards out again in three columns, but do it row by row. Now ask again which column the chosen card is in. Gather up the cards, sandwiching the indicated column between the others. Now lay out the cards row by row in three columns yet again, and you'll find that the chosen card is in the middle column, four rows down, ie the exact middle.

This trick works with any odd number of cards in each column, and it seems to work with any odd number of columns as well, but I'm not guaranteeing anything. When picking up the cards in a column, do it the way anyone would, ie by either taking the card farthest from you first and then the one nearer to you etc, or the one nearest to you first and then the one farther away etc. The key thing is to preserve the relative order of the cards in the indicated column; it doesn't matter if that order is reversed. Another important thing is to try and make it look as if you're just gathering up the cards in any old way; the audience mustn't notice that there's some kind of system. Just play it cool, chat a bit and try to give the impression that you're not even paying any attention to the cards. One last note; if you think columns take up too much space, do it in rows instead.

Good luck, although you'll hardly need it with this trick.

You have to perform the process of asking which column the card is in (and sandwich that column between the other two) three times for 3x5 and 3x7 grids, but only two times for 3x3 grids.

Don't do this trick with only one card in each column! It gets painfully obvious...