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April 09, 2022 Post a Comment

The T-puzzle, a T shape can exist assembled with the four pieces on the left.

The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital letter T. The four pieces are ordinarily one isosceles right triangle, 2 right trapezoids and an irregular shaped pentagon. Despite its apparent simplicity, it is a surprisingly hard puzzle of which the crux is the positioning of the irregular shaped piece. The earliest T puzzles date from around 1900 and were distributed equally promotional giveaways. From the 1920s wooden specimen were produced and fabricated available commercially. Nearly T puzzles come with a leaflet with additional figures to be synthetic. Which shapes can exist formed depends on the relative proportions of the different pieces.

Origins and early history [edit]

The Latin Cantankerous [edit]

The Latin cross puzzle (left) and the T puzzle (right).

The Latin cross puzzle consists of a reassembling a v-piece dissection of the cantankerous with three isosceles correct triangles, one right trapezoids and an irregular shaped six-sized piece (see figure). When the pieces of the cross puzzle have the right dimensions, they can also be put together equally a rectangle. From Chinese origin, the oldest examples date from the first half of the nineteenth century.^[1] ^[2] One of the earliest published descriptions of the puzzle appeared in 1826 in the 'Sequel to the Endless Amusement'.^[three] Many other references of the cross puzzle tin can exist constitute in amusement, puzzle and magicians books throughout the 19th century.^[four] The T puzzle is based on the cantankerous puzzle, only without head and has therefore simply four pieces. Another departure is that in the autopsy of the T, i of the triangles is usually elongated as a correct trapezoid. These changes brand the puzzle more hard and clever than the cross puzzle.^[five]

Advertizement premiums [edit]

The Lash'southward Bitters T-puzzle, the primeval known version of the puzzle

The T-puzzle became very pop in the beginning of the 20th century equally a giveaway item, with hundreds of different companies using it to promote their business or product.^[6] The pieces were made from newspaper or cardboard and served as trade cards, with advertisement printed on them. They commonly came in an envelope with instructions and an invitation to write to or call at the visitor or local dealer for its solution. Examples include:

Lash's Bitters – the original tonic laxative (1898). This is the primeval known version of the T-puzzle. The angles are cut at 35 degrees which makes the puzzle easier and less confusing.^[4]
White Rose Ceylon tea, Seeman Brothers, New York (1903).^[seven] This puzzle is often cited as being the oldest version of the T puzzle,^[5] but Lash's Bitters puzzle predates information technology.^[four]
Armour'south dry sausage, Armour and Company, Chicago. The text on the envelope reads "The Teaser T, Delight take this interesting little puzzle with our compliments. You will find it a real test to fit the four pieces enclosed in this envelope together to form this perfect alphabetic character 'T.' If you lot fail to solve it, ask your dealer for the solution. And to solve the problem of adding delicious meat dishes to your menu Enquire your dealer for Armour's Dry Sausage".^[5] ^[8]
Larabee's all-time flour (1919).^[9]
Waterall'south T Puzzle Paints & Varnishes distributed past O.J. Miller & Son, Allentown, Pennsylvania. The envelope mentions that the puzzle is "highly entertaining, interesting, perplexing, aggravating and piece of cake".^[ten]
Insurance company of Glens Falls T Puzzle, New York.^[11]

Early published references [edit]

Published references to the T-puzzle appeared in the start of the 20th century. In the Oct 1904 edition of "Chief Education", a monthly periodical for primary teachers, the T-puzzle is described equally a puzzle for tired children, and they further annotate: "Putting the letter on the lath will assistance the wee ones. They say it takes grown-ups ten minutes to fit the pieces. How long volition information technology take the children?"^[12] Another early reference is the April 1905 edition of a mag called "Our Young People".^[13] A particular nice presentation of the puzzle appeared in the October 1913 issue of John Martin's Volume, here shown to the left.^[14]

In "Carpentry & mechanics for boys" by A. Hall (1918), figures of an example T and full-size patterns are given for the construction of a wooden version of the puzzle.^[15] The arms of the T are longer than usual.^[4] The same drawings appear in "Junior Red cross activities—teachers manual" published in the same year by the American Junior Blood-red Cross.^[xvi] The puzzles presented in this volume were proposed to be constructed by blood-red cross juniors for employ in the armed forces: "to be used for distribution at canteen centers for the men passing through on the troop trains ... for employ in camps, convalescent houses and hospitals" (p. 378). They note that the puzzle "has proven pop with British Tommies" (p. 394) and give detailed instructions on how to fabricate the pieces and an envelope container.

Commercial puzzle [edit]

Pa'south T Puzzle No. P 20 WM. F. Drueke & Sons Grand Rapids, Mich.

Only the T [edit]

The T puzzle remained pop throughout the 20th century and versions of it were sold as a game puzzle as early as the 1920s'. An example dated around that time is a French version of the puzzle called "L'ÉTÉ" produced by N.K. Atlas of Paris.^[5] ^[17] Another case is the wooden version of the puzzle produced by Drueke & Sons, nether the name "Pa's T puzzle", dated around the 1940s and hither depicted to the correct.^[18] Later likewise versions were produced with plastic pieces, such as "Adams T puzzle" by S.Southward. Adams Co in the 1950s'^[18] ^[19] ^[20] and "The famous T puzzle" by Marx Toys in the 1960s-1970s.^[18] From the 1980s' dates the "Mr T's puzzle" featuring the actor Mr. T from the popular A-Team TV series; the back of the production packaging has the catchphrase "I compassion the fool who tin can't solve Mr. T'southward puzzle".^[21]

Extensions [edit]

These 160 thematically grouped shapes tin can exist formed with the commercially widespread disproportionate T version of the T puzzle.

It was recognized early on that other shapes could exist formed with the 4 pieces of the T puzzle, similar to the tangram. From the 1930 dates an advert premium for Mohawk Rugs & Carpets which besides the regular T, features the challenge of making an arrowhead with the same pieces.^[22] In the aforementioned yr a giveaway for Eberhard Faber'due south Van Dyke pencils featured fourteen different shapes to form.^[23]

At present T puzzles come in standardized proportions which allow the structure of many additional shapes. The most important designs are (run across too effigy below):

Nob's T puzzle: Designed by Nob Yoshigahara, this version of the T puzzle sold over four meg copies.^[24] The pieces can be laid out in the shape of a symmetrical convex pentagon with two right angles.^[25] ^[26] ^[27]
Asymmetric T: This T is asymmetric in that the left and correct arm of the T take different lengths, with the shorter arm being near 83% of the longer one. Here all pieces accept the same width and can exist put in a perfect line segment. At present this puzzle is for instance sold by HIQU and comes with 100 figures to brand and by Eureka Toys and Games in a puzzle called encephalon twister.^[28] ^[29]
Gardner'due south T: This is the version featured in Martin Gardner's Scientific American column.^[6] The pieces as well form a fatter T, as noted in a later cavalcade.^[thirty] ^[31] This version was sold nether the proper name "The missing T" every bit function of Aha! Encephalon teasers classics from Think Fun.^[18]

Iii common variations of the T puzzle, each with different proportions of the pieces and some other shapes which tin can exist made with the respective pieces. These other shapes are unique to each variation.

Solving the puzzle [edit]

"I know of no polygon-dissection puzzle with as few pieces that is so intractable." – Martin Gardner^[6]

With only four pieces, the T puzzle is deceitfully simple. Studies have shown that few people are able solve it nether five minutes, with most people needing more than half an hr to solve it.^[32] A common response of subjects is to conclude that the puzzle is impossible to solve.^[33]

The main difficulty in solving the puzzle is overcoming the functional fixedness of putting the pentagon piece either horizontally or vertically; and related to this, the tendency of trying to fill up the notch of the pentagon. In one written report^[32] participants were establish to spend over 60% of their attempts on such misguided placements of the pentagon piece. And fifty-fifty when the pentagon piece happened to exist placed properly, information technology was generally non recognized as part of the solution, as a friction match with the T is not easily seen. The puzzle is easily solved when the insight is reached that the pentagon is role of both the horizontal and vertical stem of the T and that the notch in the pentagon constitutes an inside corner.

Notes [edit]

^ Slocum & Botermans 1986, p. twenty.
^ The Jerry Slocum Mechanical Puzzle Collection holds a carved ivory cross puzzle dated 1820–1850: Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ A Sequel to the Countless Amusement: Containing Nigh Four Hundred Interesting Experiments, in Various Branches of Science ... to which are Added, Recreations with Cards, and a Collection of Ingenious Problems. London: T. Boys, and Thorp & Burch. 1826. p. 207. OCLC 28607491.
^ ^a ^b ^c ^d Singmaster 2000.
^ ^a ^b ^c ^d Slocum & Botermans 1986, p. 21.
^ ^a ^b ^c Gardner 1971, p. 114.
^ The White Rose T puzzle at the Image drove of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August eighteen, 2013.
^ The Armour's Teaser T at the Prototype drove of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August eighteen, 2013.
^ Larabee'southward best flour at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ Waterall's T Puzzle at the Image drove of the Slocum puzzles at The Lilly Library, Indiana Academy, Bloomington, Indiana. Accessed Baronial 18, 2013.
^ Glens Falls T Puzzle at the Prototype collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ Kellogg, Eva D., ed. (Oct 1904). "Puzzle for tired children". Primary Pedagogy. Boston: Educational Publishing Company. 12 (viii): 412.
^ "Puzzles". Our Young People. Milwaukee: St. John's Institute for Deaf-Mute. 13 (10): 751. April 1905.
^ "The big T puzzle". John Martin's Book, A Magazine for Lilliputian Children. New York: John Martin's House. 4 (one). October 1913.
^ Hall, Albert Neely (1918). Carpentry & mechanics for boys: up-to-the-minute handicraft. Boston: Lothrop, Lee & Shepard Co. p. 19. OCLC 7075900.
^ American Junior Red Cross (October 1918). Junior Red cantankerous activities; teachers transmission. New York: Press of D.C. McMurtrie. OCLC 5593504.
^ L'ÉTÉ Puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ ^a ^b ^c ^d Storer 2013.
^ Adams T puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana Academy, Bloomington, Indiana. Accessed Baronial xviii, 2013.
^ Adams T puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed Baronial xviii, 2013.
^ Mr T's puzzle at the Epitome collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed Baronial eighteen, 2013.
^ Mohawk Rugs & Carpets T puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ Mohawk Rugs & Carpets T puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed Baronial eighteen, 2013.
^ Slocum 2004.
^ Nob's T puzzle at the Image collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ Nob'due south T puzzle at the Prototype collection of the Slocum puzzles at The Lilly Library, Indiana University, Bloomington, Indiana. Accessed August 18, 2013.
^ Solutions to Nob's version of the puzzle
^ HIQU T puzzle website
^ The braintwister game and solutions for the asymmetric T puzzle
^ Gardner, Martin (Feb 1972). "Mathematical Games: Dr. Matrix poses some heteroliteral puzzles while peddling perpetual motion in Houston". Scientific American. 226 (2): 100–104. doi:ten.1038/scientificamerican0272-100.
^ von Känel, Karin & Jürg (2008). "The "T" Puzzle" (PDF) . Retrieved 16 Baronial 2013.
^ ^a ^b Suzuki, Hiroaki; Hiraki, Kazuo (1997), Constraints and their relaxation in the processes of insight. (PDF), Tokyo: Electrotechnical Laboratory
^ Finkenbinder, East. O. (1914), "The Remembrance of Problems and of Their Solutions: A Study in Logical Memory", The American Journal of Psychology, 25 (1): 32–81, doi:10.2307/1413023, hdl:2027/mdp.39015065834510, JSTOR 1413023

References [edit]

Singmaster, David (2000). "half-dozen.AQ. Dissections of a Cross, T or H". Sources in Recreational mathematics – An annotated bibliography (unpublished) (Seventh Preliminary ed.). Southward Bank Academy, London. Retrieved 31 July 2013.
Slocum, Jerry; Botermans, Jack (1986). Puzzles Old & New – How to Make and Solve Them . Seattle: Univ. of Washington Press. ISBN978-0295963501. OCLC 14414444.
Slocum, Jerry (2004). "To Takako, Rememberances [sic] by a friend" (PDF) (Eulogy). Retrieved August 18, 2013.
Gardner, Martin (Nov 1971). "Mathematical Games: Advertisement premiums to beguile the mind: classics by Sam Loyd, main puzzle‑poser". Scientific American. 225 (5): 114–121. doi:x.1038/scientificamerican1171-114.
Storer, James A. (2013). "Missing T". Retrieved sixteen August 2013.