A Binary Parlor Trick

Written by Julie Zelenski

This puzzle is reproduced from a cereal box. Thanks to CS Lecturer Nick Parlante for this trick!

Get our your scissors and prepare to win yourself a few bets with this trick. Cut out the cards below. Have a volunteer pick a number between 1 and 63, hand these cards to them, and ask them to give you back only those cards on which their chosen number appears. In a feat of amazing wizardry, you then immediately tell them what their number is. How do the cards work?

  1    3    5    7    9  11
13  15  17  19  21  23
25  27  29  31  33  35
37  39  41  43  45  47
49  51  53  55  57  59
61  63
  2    3    6    7  10  11
14  15  18  19  22  23
26  27  30  31  34  35
38  39  42  43  46  47
50  51  54  55  58  59
62  63
  4    5    6    7  12  13
14  15  20  21  22  23
28  29  30  31  36  37
38  39  44  45  46  47
52  53  54  55  60  61
62  63
  8    9  10  11  12  13
14  15  24  25  26  27
28  29  30  31  40  41
42  43  44  45  46  47
56  57  58  59  60  61
62  63
16  17  18  19  20  21
22  23  24  25  26  27
28  29  30  31  48  49
50  51  52  53  54  55
56  57  58  59  60  61
62  63
32  33  34  35  36  37
38  39  40  41  42  43
44  45  46  47  48  49
50  51  52  53  54  55
56  57  58  59  60  61
62  63