Age Cube
by Werner Miller

Werner Miller is a retired teacher of mathematics, whose hobbies are recreational mathematics and magic. A magical inventor and writer, Werner has produced a prolific volume of work, mostly what he calls “semi-automatic” card tricks based on mathematical principles. He is the author of "Fast von selbst", "Alles Miller oder was", "Ratatouille", more than 300 trick contributions to various magazines and web sites and more than 30 related computer programs. In addition, Werner is also a staff member of the German magazine "Magische Welt", a columnist for the British magazine "The Magician", and regular contributor here at Visions. Werner's first English-language book, Ear-Marked, is available here.

You are probably familiar with the so-called "Age Cards“, a set of number cards for divining a mentally selected number. There is hardly a magic book or magic kit for kids to be found that does not teach this trick, and because the secret behind is pure mathematics (the binary number system), it is discussed in many books on recreational mathematics, too.

Fig. 1 shows such a set for divining numbers from 1 to 31. Twenty years ago, I discovered that the numbers of each of these cards can be arranged to form a magic square (fig. 2). This gave me the idea for a three dimensional version of the “Age Cards” which I call “Age Cube” (fig. 3). It may be used as a neat promotional piece (put your own logo on the 6th face) and exciting give-away to would-be magicians. The reference to magic squares is a welcome misdirection to disguise the real modus operandi.

The accompanying instructions may e.g. run as follows:

I am a very special cube. Cut out my net, fold it, and paste it together. With my help you can divine a thought-of number up to 31.

Have a spectator sitting across. Place the cube before him, logo on top (you can read “Online-Visions”). The square with the “1” in the left top corner is facing the spectator, the square with the “4” in the top left corner is facing you. Ask the spectator if he can see his number on the square facing him. (When the answer is “yes”, remember the number 1.)

Give the cube a quarter turn to the right. Again, ask the spectator if he can see his number. (When the answer is “yes”, remember the number 2.)

Give the cube another quarter turn to the right, and ask again. (When the answer is “yes”, remember the number 4.)

Give the cube another quarter turn to the right, and repeat your question. (When the answer is “yes”, remember the number 8.)

Now tip the cube over toward yourself so that the bottom of the cube is facing the spectator, and for the last time, ask if the thought-of number is seen. (When the answer is “yes”, remember the number 16.)

Mentally add the numbers you remembered, and you know what number has been selected.

Finally, give the cube to the spectator as a souvenir. (And don’t forget to draw his attention to the fact, that each face of the cube is a magic square!)

Werner Miller