mathematics of party favors

True story: My wife bought a bunch of party favors for a family gathering. These were rolled up gift wrapping containing some cheap present. She opened on and found a party game labeled “The Mystery Calculator”. She gave it to me.

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This is what it is: A small folded cardboard mini-booklet of 6 cards of 4×8 arrays of numbers, ranging from 1 to 63.

Page 1:

\begin{array}{rrrrrrrr}  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  \end{array}

Page 2:

\begin{array}{rrrrrrrr}  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  \end{array}

Page 3:

\begin{array}{rrrrrrrr}  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  \end{array}

Page 4:

\begin{array}{rrrrrrrr}  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  \end{array}

Page 5:

\begin{array}{rrrrrrrr}  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  \end{array}

Page 6:

\begin{array}{rrrrrrrr}  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  \end{array}

Here are the rules to the game.

Show the 6 cards to a friend. Ask him or her secretly pick any number from any card. Tell them to look through the 6 cards and find those cards that the number they selected also appears, and give those cards to you. You add the numbers in the upper left-hand corner of these cards. This sum will be the number your friend selected.

I haven’t proven this works but my guess is that this is based on the mathematics of the Hamming code of length 6 (see this previous post and this one).

2 thoughts on “mathematics of party favors

  1. This is just based from the binary system and it works. There is also a variation out there that use the Fibonacci sequence instead.

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