The Deluxe Real Numbers Game

This game taught how to build grammatically correct expressions that represent real numbers (numbers that can be written in decimal notation, including those with infinite decimal expansions). Real Numbers was developed by Layman E. Allen at Yale University Law School as director of the ALL (Accelerated Learning of Logic) Project that developed mathematical games under a grant from the Carnegie Corporation of New York.
The game includes five wooden cubes in a holder with a ballpoint pen. On their faces the cubes have single digit numbers and symbols representing arithmetical operations (addition, subtraction, multiplication, division, as well as exponentiation, and taking roots). The game is explained in a four-page pamphlet, the REAL numbers game, written by Allen in 1966.
The pamphlet explaining the game refers to various types of real numbers including natural numbers (1,2,3 …), integers (… 3, 2, 1,0,1,2,3 …), rational numbers (numbers that can be written as a ratio of two integers with a non-zero denominator), and irrational numbers (real numbers that are not rational numbers, such as the square root of two). After rolling the dice, players attempt to write down all possible real numbers formed from the symbols and numbers shown. The pamphlet also includes rules for scoring.
The game and the pamphlet explaining it came in a plastic bag that had been stapled to a hanging display label that reads: the deluxe (/) REAL (/) numbers game by Layman E. Allen. The plastic bag also included a sheet listing “GAMES for THINKERS” that were available from WFF ‘N PROOF Publishers and a postcard offering a free one-year subscription to the WFF ‘N PROOF Newsletter.
In 1968 Allen moved from Yale to the University of Michigan with a joint appointment in the Law School and the Mental Health Research Institute, where he continued his work on instructional games. Over the years the name and location of the distributor of the Real Numbers Game changed, although the phrase “Games For Thinkers” has been associated with it from before Allen’s move to Ann Arbor. Price lists in the WFF ‘N PROOF Newsletters (part of the documentation in accession 317891) indicate that at first the game was distributed by WFF ‘N PROOF in New Haven, Connecticut, and sold for $1.50. In 1970 the price was raised to $2.00 and in 1971 the game was distributed by WFF ‘N PROOF through Maple Packers in Turtle Creek, Pennsylvania. Afirm called Learning Games Associates of Ann Arbor later took over distribution of the game and donated this example to the Smithsonian in 1975. The Accelerated Learning Foundation of Fairfield, Iowa, then became the distributor.
Reference: Games For Thinkers Website.
Currently not on view
Object Name
date made
ca 1966
Allen, Layman E.
Learning Games Associates
Physical Description
plastic (overall material)
wood (overall material)
paper (overall material)
overall: 2 cm x 15.5 cm x 12 cm; 25/32 in x 6 3/32 in x 4 23/32 in
place made
United States: Michigan, Ann Arbor
ID Number
accession number
catalog number
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Mathematical Recreations
Data Source
National Museum of American History, Kenneth E. Behring Center


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