Ann Arbor Magic Club

IBM 210 - SAM 88

Mathamagically Speaking

This month we have a special edition to the Messenger. Our resident Mathemagician, Bob Goodwin will periodically be sharing math related magic, methods, products and puzzles with us. This month Bob and Karl collaborated on a method for forcing a number, dubbed by Bob as "The Stack Force"

The Stack Force;

A Handy Tool for Mentalism & Mind Reading

Developed and written by Bob Goodwin
Edited by Karl Rabe
Spreadsheet calculation utility by Karl Rabe
Copyright 2022 by Robert Goodwin. All rights reserved.

The Stack Force enables you to force a predetermined number on a spectator by having them select several numbers from a list.  No matter what numbers they select, the total will be the force number.

Examples of numbers you may want to force:

  • Year in which a significant event occurred (Houdini's birth - 1874)
  • Anniversary (S.A.M. formed in 1902)
  • Specific word in a book ("book test")
  • Military unit designation (101st)
  • Addresses
  • Phone numbers

References and Acknowledgements

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

In “Secrets Of Mental Math", (A. Benjamin & M. Shermer, 2006 p.212) teaches an effect called AN “AMAZING” SUM. Per the authors, it was first shown to them by James “the Amaz- ing” Randi, who has used it effectively in his magic. The forcing of a single number is described.

I have “reverse engineered” this, so to speak, to provide a step-by-step guide to calculating the necessary numbers to force ANY four or five digit number you choose.

Worksheet Example of a Stack Force Routine


Houdini's Spirit Is Asking From The 'Other Side': "When was I born?"

  1. Choose one number from each category
7 1 9 8 8 0 4 8 2
7 6 4 6 2 8 7 6 1
9 4 4 0 7 9 3 9 2
3 8 6 5 4 7 5 4 5
5 8 4 3 7 6 8 2 4
  1. Add Your Chosen Numbers Here. The numbers are “stacked” vertically, not written horizontally. So for example, 719 chosen from column A is written vertically in column A below.
= Houdini Birth Year



  • This routine is based on the birth year of Houdini (1874).
  • Try it yourself. No matter what combination of numbers you choose from A, B and C they will always add to 1874.
  • The numbers shown above were developed using the target calculated using the method explained below – The digits of the numbers in Category A all add to 17, the digits of the numbers in Category B all add to 16, and likewise, the digits of the numbers in Category C all add to 14.

How To Set Up A Stack Force To Force A Certain Number


Step Number Example
- a b c
1 Identify the Target Force Number:   3-4 digits work best. 1 8 7 4

This 4-digit target is based on the year Harry Houdini was born. With a 4-digit target, 3 columns are needed (labeled A, B, & C) to stack vertically and add the numbers.


2 Calculate the number totals needed in each column to force the number:  Work from right to left, and top to bottom. Select numbers so the sum of the digits in each column add to the target number for that column. 1 4 This # is same as last # in force no., with 1 preceding (col. C)
1 6 Next # is 6, with 1 preceding (col. B).
1 7 Next # is 7, with 1 preceding (col. A).
1 8 7 4 Target # totals (14, 16, & 17) add to 1874
3 Confirm the column targets by adding some sample numbers and checking the total. 7 8 4 #s in col. C add to target (14)
1 8 8 #s in col. B add to target (16)
9 0 2 #s in col. A add to target (17)
1 8 7 4

After confirming the numbers needed for your stack force (step 3), you now need to prepare the worksheet to be reviewed with the volunteer during your routine -- see Worksheet Example of a Stack Force Routine above for an example.

You may find that some target force numbers don't require different numbers in the columns. If your calculation in Step 2 above results in the same value for all three numbers. (Example: A target of 1776 will require all three numbers to have digits adding to 16.  In this case, you do not need to have three categories of numbers. All numbers the spectator choose can be lumped together in one group.

Stack Force Calculator

This section by Karl Rabe.

After editing Bob's Stack Force above, I began playing around with Excel to see if I could automate the calculations. The result was the Stack Force Calculator spreadsheet. Click the icon below to open it. You have to enable macros and of course you need to have Microsoft Excel installed.



The Stack Force Calculator will automatically generate a set of "choice" numbers to force a desired target
number as per Bob Goodwin's method for creating a stack force. On the Stack Calc tab, enter the desired force number in the yellow cell. Any number up to 10 digits can be used. The calculcate will generate all possible choice number to use. Select your numbers from the list for each digit. You can view the Tester tab which will show the manually calculated result for each set of choices.

Here is an example of the output of the calculator, using the force number in Bob's example above, Houdini's Year 1874. You can see it produces the same target totals... 14, 16 and 17. It then provides 20 (only 10 shown here) randomly generated 3 digit numbers where the digits add to those target totals.

If you are even just a little comfortable with excel, give it a try.


Column 1 2 3
Target 14 16 17
Choice 1 590 565 359
Choice 2 752 556 584
Choice 3 707 448 944
Choice 4 860 196 566
Choice 5 428 565 575
Choice 6 905 529 386
Choice 7 824 367 629
Choice 8 914 880 719
Choice 9 653 880 476
Choice 10 365 178 368



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