Predicting Sums

Published on Sunday, June 02, 2013 in , , , , ,

Konrad Jacobs' photo of Martin GarnderIn today's post, we're going to look at a number trick presented by James Grime.

You predict the total of several 4-digit numbers, but don't worry. It's fun, simple, and straightforward.

The following routine is a quick video from the Numberphile series of videos:

The most commonly-used source for this routine is Martin Gardner's book, Mathematics, Magic & Mystery, in which it has the simple title of “Predicting A Sum”. Interestingly, the example number used in the book is 3,845, very close to James Grime's chosen example number, 3,485.

There are many ways to make this routine more impressive. You could employ a secret help, who provides the needed numbers at each step. This takes the heat off of your choices, and makes the whole routine seem fairer, and more impressive.

Another idea to consider is that you don't have to do this as a prediction. Instead, you can do it as a feat of mental arithmetic. Have two people, one of whom is your secret helper, write the numbers down out of your view, and then show the numbers to you briefly. You apparently quickly memorize and calculate the numbers in your head faster than they can do it with a calculator!

With a little creativity, you can think of numerous ways to perform this. Want to seem psychic? Divine the total without ever seeing the numbers (thanks to your secret helper again). You could also perform a routine similar to Scam School's first Pi Day Magic Trick, in which they circle a number, read off the remaining digits, and you can determine the digit or digits they didn't name. Since you know in advance what the total will be, it's all recall with no calculation!

There's a routine with a similar basis called “Alberti's Game”, in which you and two other people randomly choose 3-digit numbers to create 2 multiplication problems, and you're able to predict the sum of the answers to those multiplication problems. Because there's several steps involved, and the answers tend to be large 6-digit numbers, this version seems even more impressive.

How is it done? The answer is below, courtesy of Karl Fulves' Self-Working Number Magic (Amazon link):

Just as with the previous routine, a little creativity, and the possible secret helper, can yield some very amazing results.

Try these out, and if you like them,show your appreciation to Grey Matters by buying Martin Gardner's book, Mathematics, Magic & Mystery and/or Karl Fulves' Self-Working Number Magic. You'll find an amazing variety of number-based magic in both of these mathemagical classics!

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