Description
In the classic version of this magic trick, the magician asks one spectator thinking of
an integer between 0 and 15 and keeping it in his mind. Then the spectator is allowed to
ask four yes-or-no questions that whether the chosen number appears on the four cards.
After that, the magician will immediately know what is the number in spectator’s mind.
The secret mainly depends on 1-disjunct matrix in group testing. Theoretically, this trick
can be extended to any numbers with question cards.
Richard Ehrenborg [1] and Todd Mateer [2] modified this trick to the version that
the spectator is allowed to lie at most once by asking more questions. These question
cards are encoded by the Hamming code. The former 4 question cards are correspondent
to the 4 information bits of -code, and the new 3 cards are the 3 parity-check bits. In
general, for any positive integer, the magician also needs question cards. In this talk, we
reduce the number of question cards. Actually, we need only 1 base card and 1 question
card.
References
1. Richard Ehrenborg, Decoding the Hamming Code, Math Horizons, 13(4) 2006
17-18. doi:10.1080/10724117.2006.11974646.
2. Todd Mateer, A Magic Trick Based on the Hamming Code, Math Horizons, 21(2)
2013 9-11. doi: 10.4169/mathhorizons.21.2.9.