Olive C. Hazlett: Music and Puzzles

Photograph of Olive C. Hazlett
Olive C. Hazlett. Photograph courtesy of LHM Institute. (AHB2012q06024)

Olive Clio Hazlett (1890-1974)was a leading American mathematician of the 1920s. She was the most prolific of the US-born women of her time who worked in pure mathematics and was recognized for her research accomplishments when, in 1927, she became the second US-born woman to be ranked as one of American’s leading mathematicians by her peers, a distinction marked by a “star” in American Men of Science. In 1984, Hazlett was one of three mathematicians whose lives were celebrated in an exhibit NMAH.

Hazlett, who was awarded a PhD in mathematics from the University of Chicago in 1915, spent a postdoctoral year at Harvard University before she began her teaching career at Bryn Mawr. In 1918 she moved to Mount Holyoke and seven years later she moved to the University of Illinois.

As with most people, mathematicians have interests outside their profession. Among mathematicians, including Hazlett, these outside interests often relate to music and puzzles. Among objects in the collections that were displayed in 1984 are her tenor recorder, a set of dominoes with more spots than one sees on most domino sets, and twelve Japanese interlocking wooden puzzles called “Kumiki.”

Image of the display
“Commemorating American Mathematics,” 1984 Exhibit at NMAH. (84-5347-2)
Olive C. Hazlett (1890–1974), a leading American mathematician of the 1920s, received this wooden tenor recorder from the family of astronomer Harlow Shapley (1885–1972) .
Description
Olive C. Hazlett (1890–1974), a leading American mathematician of the 1920s, received this wooden tenor recorder from the family of astronomer Harlow Shapley (1885–1972) . Hazlett gave the recorder to a mathematician, Grace Shover (1906–1998), whom she had befriended at national mathematics meetings. Grace Shover Quinn and her physicist husband, Robert B. Quinn (1907–1993), gave the instrument and its instruction book to the Smithsonian Institution in 1983.
Location
Currently not on view
ID Number
1983.0873.01
accession number
1983.0873
catalog number
1983.0873.01
This set of Double Twelve Express Dominoes was made by the Embossing Company, an Albany, N.Y., firm that produced wooden blocks and puzzles. A sheet of instructions, “HOW TO PLAY DOMINOES,” is included in the box of ninety-six rectangular tiles.
Description
This set of Double Twelve Express Dominoes was made by the Embossing Company, an Albany, N.Y., firm that produced wooden blocks and puzzles. A sheet of instructions, “HOW TO PLAY DOMINOES,” is included in the box of ninety-six rectangular tiles. Five of these are completely blank and ninety-one are made up of two squares with each square either blank or marked with up to 12 spots, usually called pips.
The traditional American domino set is called Double Six, because each rectangular tile is made up of two squares with each square blank or marked with 1, 2, 3, 4, 5, or 6 pips. In a Double Six set, one can see seven different types of tile depending on the smallest number of pips in one of its squares. If the smallest number of pips is 0, at least one square is blank and there are seven possibilities for the number of pips in the other square, i.e., 0 through 6. If the smallest number of pips is 1, neither square is blank and at least one square has a single pip. In this case there are six possibilities for the number of pips in the other square, i.e., 1 through 6. In general when the smallest number of pips that appear on a square of a tile is k, the other square must have k, k+1, …, 6 pips on it, and it is always the case that there are 7-k numbers on the list k, k+1, …, 6. If we look at all be seven possible types of tiles in a Double Six set, we find that there are 7+6+5+4+3+2+1=28 tiles.
A similar computation can be done for any Double n set of dominoes. I.e., there are n+1 tiles with one or both squares blank, n tiles with no blanks and 1 the smallest number of pips, and n+1-k tiles with no blanks and k the smallest number of pips. This leads to a total of (n+1)+ n+(n-1)+…+1 tiles, i.e., the sum of the first n+1 integers. A mathematical formula known for many centuries says that the sum of the first n integers is n(n+1)/2 so the sum of the first n+1 integers is (n+1)(n+2)/2. For a set of Double Six dominoes n+1 is 7 so we get (7)(8)/2 or 28 tiles. Other common Double n sets include Double Nine, Double Twelve, Double Fifteen, and Double Eighteen. For the Double Twelve set, n+1 is 13 so there are (13)(14)/2 or 91 tiles. In order not to leave empty space in the box, five completely blank tiles were included in this set of Double Twelve dominoes.
These dominoes belonged to Olive C. Hazlett (1890–1974), one of America's leading mathematicians during the 1920s. Hazlett taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, N.H. Her set of dominoes was collected from the Carmelite community of Leadore, Idaho. Brothers from this community who had lived in New Hampshire had befriended Hazlett there.
Location
Currently not on view
date made
ca 1920
maker
Embossing Company
ID Number
1998.0314.01
accession number
1998.0314
catalog number
1998.0314.01
This wire puzzle, a Chinese Nine Linked Rings Puzzle, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This wire puzzle, a Chinese Nine Linked Rings Puzzle, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
There is nothing on the puzzle itself that indicates when, where, or by whom it was made.
The object of a Chinese Linked Ring Puzzle is to remove all the rings from a bar with a long slot in it. Chinese references to unlinking linked rings go back over two thousand years. Although this type of puzzle is called a Linked Ring Puzzle, the rings are not directly linked. Rather, each ring is attached to a metal wire and the ring can be removed from the bar only when that wire no longer passes through the long slot of the bar. In the early 20th century this type of puzzle was often sold with two rings that could be slipped off the bar, as in this case; the normal starting position is when only one ring can be slipped off.
Except for the ring that will be removed first, each ring has the wire of an adjacent ring going through it. All of the wires are attached to a second, often much smaller, bar from which they cannot be removed. At least two well-known European mathematicians, Girolamo Cardano (1501–1576) and John Wallis (1616–1703), unsuccessfully tried to find an analysis that would yield the smallest number of steps it would take to remove all the rings in a puzzle as a function of the number of rings. A solution to that problem was known by the late 19th century. If the starting position has only one ring that can be slipped off, a linked ring puzzle with nine rings cannot be solved in fewer than 341 steps. The mathematics involved in the analysis is related to binary reflected codes, also known as Gray codes since they were described in Frank Gray’s 1953 patent involving coding of a message signal.
Location
Currently not on view
ID Number
2015.0027.01
accession number
2015.0027
catalog number
2015.0027.01
These twelve interlocking three-dimensional wooden puzzles were made in Japan, likely by the Yamanaka Kumiki Works. Each is individually wrapped in plastic and includes a sheet showing how to assemble it.
Description
These twelve interlocking three-dimensional wooden puzzles were made in Japan, likely by the Yamanaka Kumiki Works. Each is individually wrapped in plastic and includes a sheet showing how to assemble it. A trademark on the bottom of the box includes an image of a globe surrounded by the letters T T N Y. According a 1978 application to the US Patent and Trademark Office by the Traveler Trading Company, Inc., the mark was first used in commerce in 1950. Since imports from Japan between 1945 and 1952 had to be labeled “Made in occupied Japan” and the labels on the box, the puzzles, and the instructions, all read “Made in Japan,” these puzzles were imported into the United States some time after 1952.
These types of Japanese puzzles are called “kumiki” and are said to be related to the traditional construction of wooden buildings that did not use nails or glue. This particular set includes four familiar geometrical shapes (a sphere, a cube, a barrel, and an octagonal prism), four animals (an elephant, a pig, a bird, and a dog), and four shapes without common names. Only the dog and one of the unnamed shapes are unassembled.
These kumiki puzzles belonged to Olive C. Hazlett (1890–1974), one of America's leading mathematicians during the 1920s. Hazlett taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. The puzzles were collected from the Carmelite community of Leadore, Idaho. Brothers from this community had lived in New Hampshire earlier, and befriended Hazlett there.
REFERENCE: Jerry Slocum and Rik van Grol, “Early Japanese Export Puzzles: 1860s to 1960s,” in Puzzlers’ Tribute: A Feast for the Mind, eds. David Wolfe and Tom Rodgers (Natick, MA: A. K. Peters, 2002): pp. 257-71.
Location
Currently not on view
date made
ca 1955
ID Number
1998.0314.02
accession number
1998.0314
catalog number
1998.0314.02
This example of Adders, a set of four puzzles, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This example of Adders, a set of four puzzles, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
Adders was made by the Douglass Novelty Company of Detroit, Michigan, and sold for ten cents. The box contains a shiny green cardboard playing board and twelve small silver cardboard discs, three blank and the others numbered 1 through 9. The directions for the four different puzzles are printed on the inside of the cover of the box. The playing board is square and has various lines and circles marked on it. Three of the four puzzles involve placing the numbered discs in specified ways so that specified sets of discs add to a given number.
Adders was probably made in about 1930, since another set of puzzles in the collections, Kangaroo (2015.0027.07), was made about then by the same company and has very similar packaging, playing board, and discs.
The first puzzle has many solutions, all of which are related to the three-by-three magic square, which is known as the Lo Shu square. That square—in which the rows, columns, and diagonals all add up to 15—appears in Chinese literature dating back to 650 BCE. Some of the solutions are equivalent to the Lo Shu square, and all the other solutions can be derived from a solution equivalent to the Lo Shu square by switching two discs, neither of which lies in the center of the circle, but are on the same line through the center of the circle.
Location
Currently not on view
date made
ca 1930
maker
Douglass Novelty Company, Inc.
ID Number
2015.0027.02
accession number
2015.0027
catalog number
2015.0027.02
The book Mathematical Puzzles and Pastimes was obtained by Olive C. Hazlett (1890–1974) on May 27, 1965. Hazlett was one of America's leading mathematicians during the 1920s.
Description
The book Mathematical Puzzles and Pastimes was obtained by Olive C. Hazlett (1890–1974) on May 27, 1965. Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This volume, as well as other puzzle books and puzzles she owned, was collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
The puzzles and pastimes of the book were gathered and edited by Philip Haber and illustrated by Stanley Wyatt. The book was published by The Peter Pauper Press of Mount Vernon, New York, in 1957. Haber collected problems that he wrote could “be solved primarily by clear thinking, arithmetic or algebra.” The book contains 113 problems with solutions given to some of them. Haber refers to the last four problems as “famous” and gives their names as: The Impossible Division Problem, The Unit Problem, The Apple Problem, and The Problem of Problems (Archimedes’ Cattle Problem).
Hazlett wrote “$1. for 3” on the title page of this book. There is one other book in the museum collections, The Little Riddle Book (2015.3004.02), that was also published by The Peter Pauper Press and also obtained by Hazlett on May 27, 1965. In that book she wrote “3 for $1.” Hazlett signed her name “O. C. Hazlett” on the dustcover of both books. She made other handwritten marks in Mathematical Puzzles and Pastimes, including several whose meanings are not clear.
Location
Currently not on view
date made
1957
ID Number
2015.0027.03
accession number
2015.0027
catalog number
2015.0027.03
This example of Dad’s Puzzler belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This example of Dad’s Puzzler belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
This puzzle, which was copyrighted by J. W. Hayward in 1926, was manufactured by The Standard Trailer Company of Cambridge Springs, Pennsylvania. According to Around Cambridge Springs by Sharon Smith Crisman and the Cambridge Springs Historical Society, the Standard Trailer Company “originally made wagons for hauling goods” but made both Dad’s Puzzler and Ma’s Puzzle during the Great Depression (Arcadia Publishing, 2003, p. 92).
Dad’s Puzzler is a solitaire game of a type known as a sliding block puzzle. It consists of one two-by-two square, four two-by-one rectangles with the long side horizontal, two two-by-one rectangles with the long side vertical, and twoone-by-one squares. Like the best known puzzle of this type, the Fifteen Puzzle (first described in the late 19th century), the object of the game is to move blocks from one arrangement to a given final arrangement. Unlike the Fifteen Puzzle, which does not have a given starting arrangement, the starting arrangement of Dad’s Puzzler is shown on the cover of the box. Also unlike the modern Fifteen Puzzle, the blocks are not all of the same shape. Although Dad’s Puzzler blocks are not fastened to the box, the rules of the game as given on the cover of the box specify that the blocks must be moved “without jumping or raising any block from [the] bottom of the box or turning any piece.” Over the years, many versions of this puzzle have been distributed as an advertisement, often by moving companies.
The lid of the box indicates that a patent for Dad’s Puzzler had been applied for. However, in December 1907, L. W. Hardy had applied for a patent for a sliding block puzzle with the same shaped blocks as those of the later Dad’s Puzzler. The earlier patent application was for a “new and useful Improvement of Puzzle in puzzles” that stressed the number of pieces of each specific shape. These differ from those of Dad’s Puzzler, which replaced two one-by-one squares in Hardy’s version with a rectangle. The earlier patent application resulted in a patent being issued in February 1912.
Martin Gardner referred to Dad’s Puzzler in his February 1964 Mathematical Games column in the Scientific American, “The hypnotic fascination of sliding-block puzzles” (vol. 210, pp. 122–130), noting that it soon became known as Dad’s Puzzle. He also noted that the mathematical theory about which starting positions of the Fifteen Puzzle would lead to a solution did not apply to sliding block puzzles, such as Dad’s Puzzler, when the pieces were not all squares of the same size. It has since been proven that there can be no comparably simple theory that applies to all sliding block puzzles.
Location
Currently not on view
date made
ca 1928
ID Number
2015.0027.04
accession number
2015.0027
catalog number
2015.0027.04
This example of Mystery Maze belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This example of Mystery Maze belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
On the back of this puzzle there are marks that indicate that it was manufactured by the Harmonic Reed Corporation of Philadelphia, Pennsylvania, and that a patent had been applied for. The following description of the puzzle appears in the February 3, 1951, issue of The Billboard: The Amusement Industry’s Leading Newsweekly on page 66 under Merchandise Topics: “To retail for 50 cents, Harmonic Reed Corporation has introduced its Mystery Maze puzzle. The plastic tilt puzzle, with clear top and standard beebee ball, has the unusual feature of a concealed section. Though unseen by the player, the ball must pass thru this section to reach the finish. However, if a mistake is made, the ball will not go farther and must be returned to the puzzle’s starting point before another try at the concealed section can be made.”
Location
Currently not on view
date made
1951
maker
Harmonic Reed Corporation
ID Number
2015.0027.05
accession number
2015.0027
catalog number
2015.0027.05
This example of Word Puzzle belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This example of Word Puzzle belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
This puzzle was made in Hong Kong, probably in the early 1950s. It is a solitaire game known as a sliding block puzzle and looks very much like the best known sliding block puzzle, the Fifteen Puzzle, which was first described in the late nineteenth century. The aim of Fifteen Puzzle is to slide the pieces from a given starting position to get the four rows to read 1 through 15 with the blank space at the bottom right corner. Unlike the Fifteen Puzzle there is more than one solution to this Word Puzzle since the aim is to move the letters around to form as many words as possible.
In the late 19th century mathematicians proved how to determine which starting positions of the Fifteen Puzzle would lead to a solution. In particular, if the starting position in the first three rows read 1 through 12 while the fourth reads 13, 15, 14, blank, the puzzle cannot be solved. This is known as the “14-15 Puzzle of Sam Loyd” even though the puzzle author Sam Loyd first mentioned it, and challenged players to solve it, well after it had been shown to be unsolvable.
This Word Puzzle has as one of its solutions RATE YOUR MIND PAL, and for some time there were sliding block word puzzles sold showing a starting position of RATE YOUR MIND PLA to mimic Sam Loyd’s 14-15 Puzzle. However, unlike the Fifteen Puzzle, whose fifteen squares have no repetitions, this puzzle has two A’s as well as two R’s. Since the mathematical analysis of the Fifteen Puzzle implies that if there is a repetition of at least one marking on a square, then the fifteen squares can be arranged in any order you choose, this Word Puzzle can be solved either as RATE YOUR MIND PAL or RATE YOUR MIND PLA.
Location
Currently not on view
ID Number
2015.0027.06
accession number
2015.0027
catalog number
2015.0027.06
This example of Kangaroo, a set of three puzzles, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s.
Description
This example of Kangaroo, a set of three puzzles, belonged to Olive C. Hazlett (1890–1974). Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This and other of her puzzles and books of puzzles were collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.
Kangaroo was made by the Douglass Novelty Company of Detroit, Michigan and sold for ten cents. It is listed in American Game Collectors Association’s The Game Catalog: U.S. Games Through 1950 (8th ed., Oct. 1998, p. 40) as having been made in about 1930.
The box contains a shiny orange cardboard playing board and twelve, six gold and six silver, small blank cardboard discs. The directions for the three different puzzles are printed on the inside of the cover of the box. The playing board is square and has small circles and squares marked on it. There are also two rows of number marked, one runs from 1 to 10 and the other runs from 1 to 8. The directions for each puzzle specify a starting position, the rules for moving the discs (including jumping), and the required final position of discs.
The first puzzle was a popular puzzle described by W. W. Rouse Ball in his Mathematical Recreations and Essays. The other two are related to another puzzle described by Rouse Ball and ascribed to P. G. Tait, a 19th-century Scottish mathematician remembered for his work in knot theory.
Location
Currently not on view
date made
ca 1930
maker
Douglass Novelty Company, Inc.
ID Number
2015.0027.07
accession number
2015.0027
catalog number
2015.0027.07

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