Ann Arbor Magic Club

IBM 210 - SAM 88

Mathamagically Speaking #5

Mathematically Speaking #5
The Force Square
Bob Goodwin

This month we will explore something known as a Force Square. The Force Square allows you to force a particular number by seeming random selections made by a spectator from a matrix of numbers.


How to create a force square

Step Action Example
1 Select your force number 45
2 Choose two numbers that add to your force number. These numbers become your row and column totals. 20, 25
3 Select four number that add to your row total and fill them in the boxes below A, B, C & D 5+3+8+9=25
4 Select four numbers that add to your column total and fill them in the boxes to the right of 1, 2, 3 & 4 4+6+2+8=20
5 Now populate each blue box with the sum of it's row header and column header. 5+4=9
6 The blue squares are now your Magic Square to force the number 45. Replicate just the magic square portion on whatever you are going to use for your performance.



A B C D Tot
5 3 8 9 25
1 4 9 7 12 13
2 6 11 9 14 15
3 2 7 5 10 11
4 8 13 11 16 17
Tot 20


How to use the force square

9 7 12 13
11 9 14 15
7 5 10 11
13 11 16 17

This is a bare bones description of how to use the force square. We will go through a presentation example below.

  1. Give the spectator a sheet of paper with the force square printed on it and a pen.
  2. Ask the spectator to circle any four numbers, but each number they circle must be in a different row AND column from any other number.
  3. Have them total the circled numbers. It will always equal the force number.




  1. Prepare a force square that adds to the number $210. Dress it up with additional columns as illustrated below.
  2. Prepare a prediction that reads "I predict that the total cost of your Egypt transportation is $210. Put this in a sealed envelope.
From To Camel Chariot Uber Boat
Selected Cost
Amarna Luxor $55 $45 $65 $35
Luxor Aswan $40 $30 $50 $20
Aswan Giza $60 $50 $70 $40
Giza Amarna $75 $65 $85 $55



  1. Ask an audience member to hold your prediction.
  2. Select a volunteer and explain to them that, while vacationing in Egypt, you want to use the four types of transportation to travel to the four cities shown.
  3. Ask the volunteer to select the type of transportation they would like to use from Amarna to Luxor. Tell them they will only be able to use each type of transportation once. Whatever they pick, circle that amount and write the amount in the selected cost column.
  4. Repeat for each leg of the journey. Remind them that they cannot use the same transportation twice.
  5. When all legs have been selected total the column.
  6. Reveal that the total matches your prediction.

You could add interest to the reveal by having stage money in the envelope totaling $210. Put a big $ on the front. Tell them in advance that the envelope has all the money you have budgeted, and you hope they can stay within budget.

This principle can be "dressed up" in many ways. Cost of menu items from appetizer, salad, entree and desert, for example.

What other presentations can you think of?

Edited by Karl Rabe

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