In the matrix force, numbers (or in certain applications other entities) are arranged in a square X-times-X matrix. The following procedure to choose X numbers is then used: Any number is freely chosen and all other numbers in the same row and column are crossed out and eliminated. This is repeated with one of the remaining available numbers. When this is continued until X numbers are chosen and those are added, the result is a pre-determined force number.

This is made possible by a special arrangement of the numbers in the form of an addition table and was first recorded by Maurice Kraitchik in his *Mathematical Recreations*, 1942, p. 184. Martin Gardner also describes work on the force in the chapter “Calendars” in *Mathematics, Magic And Mystery*, 1956, p. 48, including Mel Stover's “Stover's Prediction”. In his Mathematical Games column “A new kind of magic square with remarkable properties” Gardner offered a more substantial discussion of its mathematical properties, see *Scientific American*, Jan. 1957. (This has been reprinted in the 1959 collection *The Scientific American Book of Mathematical Puzzles and Games* (retitled in 1988 as *Hexaflexagons and Other Mathematical Diversions*), p. 15, “Magic with a Matrix”.)

One can avoid an actual matrix by putting each column as a list of numbers on a separate piece of paper. The positions of the numbers are then assigned different properties (color, position numbers, etc), e.g. the top number on every paper is green, the next blue, and so on. When now one number is chosen from each list, and all must have different colors, one is doing the Matrix Force procedure in a different way and arrives at the force number.

This variation was used by Karlheinz Krummel as “Die Zahlentafeln des Pythagoras” in *Magie*, Aug. 1971, Vol. 51 No. 8, p. 208. A later version in English language is Paul John Flory's “The 5040 Prediction” in *The Linking Ring*, Vol. 61 No. 2, Feb. 1981, p.67.

This type of force has been used for the Menu Bill Prediction by assigning different courses to the positions on the lists.

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