Puzzle, Bali-Buttons


This puzzle consists of a square black plastic base with a 4x4 array of pegs on it. The pieces come in four different colors (red, blue, green, and yellow) and four different shapes (circle, square, triangle, and octagon). One piece, the red triangle, is missing. The goal of the puzzle is to arrange the pieces so that there are four pieces of different shapes and different colors in every, row, column and diagonal. An explanation on paper is inset into the back of the base.

The explanation that accompanies the puzzle includes a description of a legend about how Balinese villages of single person huts arranged and occupied so as to protect families from damage caused by a fallen tree during a typhoon. There are four families each of which include only a father, mother, son, and daughter and 16 huts are laid out in a square with every line of 4 huts contains members of each family and a father, mother, son, and daughter.

However, the final paragraph of the explanation includes the statement, “This legend becomes effective January 15, 1969.” The effective date is based on the granting of a copyright in 1968 to a Palo Alto, California, firm, Products of the Behavioral Sciences, Inc., for a pamphlet with the title “Bali-Buttons, the legend and the puzzle.”

While the legend has no history, the mathematical problem on which this puzzle is based has been known for centuries as the Magic Card Square (Ozanan. Récréations mathématiques et physiques, 1723 edition, vol. IV, p. 434). It is also related to Euler’s Officers Problem that had been posed by the 18th century mathematician Leonhard Euler when he was in his 70s. That problem used ranks and regiments of six groups of six officers instead shapes and colors of four groups of four puzzle pieces and only assumed that the rows and columns of the square could not repeat a rank or regiment. Euler conjectured that his problem was not solvable but was only proved in 1901 by and French amateur mathematician, Gaston Tarry.

The name of the puzzle that appears on the explanation is entirely capitalized, e.g. it reads: BALI-BUTTONS.


W. W. Rouse Ball, revised by H. S. M. Coxeter, Mathematical Recreations and Essays. NY: Macmillan Co., 1947, pp 189-92.

Date Made: 1969?

Maker: Behavioral Sciences, Inc.

Location: Currently not on view

Place Made: United States: California, Palo Alto

Subject: MathematicsMathematical Recreations


See more items in: Medicine and Science: Mathematics


Exhibition Location:

Credit Line: Gift of Sherman L. and Marjorie A. Naidorf

Data Source: National Museum of American History

Id Number: 2005.3024.001Catalog Number: 2005.3024.001Nonaccession Number: 2005.3024

Object Name: puzzle

Measurements: overall: 1.8 cm x 12.5 cm x 12.5 cm; 23/32 in x 4 29/32 in x 4 29/32 in

Guid: http://n2t.net/ark:/65665/ng49ca746ab-b497-704b-e053-15f76fa0b4fa

Record Id: nmah_1292821

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