Lined Up
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 semi-automatic card tricks and other self-working miracles. He is the author of "E-Z Square 1 & 2", the "Enigmaths" series and several other books and ebooks on mathematical magic, besides more than 300 contributions to various magazines and web sites. You can find his tricks regulary in, e.g., the German magazine "Magische Welt" and the British "Mystery Magazine", as well as here at Visions.

Here’s a lightweight calculation stunt you may like.

Get six variously colored dice. Arrange them as shown below so that each die is showing an unique number of spots. Have the numbers in ascending order.

Turn your back.

Request a spectator to turn any die over. Then ask him to add up the six top numbers and to announce the total. You can immediately tell which die has been turned over.

Have the original arrangement restored. Offer a repetition, but this time instruct the spectator to turn over the five not selected dice before adding up the six top numbers. As soon as the total is announced, you know the selected die again.

Here’s how:
Example 1: The spectator selects the red die (3) and turns it over. The total of the top numbers is now 1 + 2 + 4 + 4 + 5 + 6 = 22. To trace back to 3, mentally divide the announced total by 2 and subtract the result from 14.

Example 2: The spectator selects the yellow die (2) and turns the five other dies over. The total of the top numbers is now 6 + 2 + 4 + 3 + 2 + 1 = 18. To trace back to 2, mentally divide the annonced total by 2 and subtract 7.

Because it’s more impressive to reveal the color of the selected die than the number of spots originally atop, it is advisable to memorize the colors of the lined-up dies in ascending order (1 = white, 2 = yellow, 3 = red, 4 = blue, 5 = green, 6 = black).

Don’t be afraid of math!

Werner Miller