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Lagrange 1 of 22 the Great Mathematical Puzzelist Samuel Loyd Was Born in Philadelphia, Pennsylvania in 1841 (O'conner). He Wa

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Lagrange 1 of 22 the Great Mathematical Puzzelist Samuel Loyd Was Born in Philadelphia, Pennsylvania in 1841 (O'conner). He Wa LaGrange 1 of 22 The great mathematical puzzelist Samuel Loyd was born in Philadelphia, Pennsylvania ’Conner). He was the youngest of nine children. At the age of three, his family moved in 1841 (O to New York where he attended public school (Carter). Sam Loyd got his start in the puzzle business with chess. At 14 years of age, Loyd started attending chess club with two of his older “New brothers. On April 14th, that same year, Loyd had his first chess problem published in the ” In 1856, the “New York Clipper” published another of his chess York Saturday Courier. ’Conner). At first, all of Loyd’s puzzles were hobbies. problems for which he won a prize (O After school he studied engineering and earned a license in steam and mechanical engineering (Loyd). For a time, Loyd supported himself as a plumbing contractor and the owner of a chain of ’Conner). Plus, music stores. He was also a skilled cartoonist and a self taught wood engraver (O he was skilled in conjuring, mimicry, ventriloquism and silhouette cutting (Gardner). Eventually, Loyd left plumbing behind and focused on mathematical puzzles. He attended chess tournaments, wrote and edited mechanical journals along with his magazine “Sam Loyd’s Puzzle Magazine” (O’Conner). For a while, he also edited the magazine entitled “Chess Monthly” and the chess page of “Scientific American” (Gardner). P. T. Barnum’s Trick ’Conner). This sale alone Donkey was invented by Sam Loyd and sold to Barnum in 1870 (O grossed $10,000 for Loyd (Carter). In 1878 Loyd published his one and only hard cover book Chess Strategy, which included all the chess problems published in Scientific American plus ’Conner). Although famous for his chess some new ones. There were 500 problems in all (O ’s popularity grew even more with his mathematical recreation puzzles. problems Loyd “14-15 Sliding Puzzle.” His most famous puzzle is also his most controversial. It is the The puzzle was a sliding puzzle with 15 little tiles in a wooden tray that could fit 16 tiles. All the tiles were numbered in order from 1 to 13. The last two tiles were 15 and 14. The puzzle was to LaGrange 2 of 22 move the tiles one at a time until all the tiles were in correct order from 1-15. Sam Loyd offered $1000 to the first person who could solve it correctly. Loyd claims to have invented the puzzle in ’Conner). Others believe Loyd was not the first to invent the puzzle, switch the 14 1878 (O th and 15th tiles, or offer $1000 as prize money. Jerry Slocum, in 2006, released a book to Mathworld about the topic. According to him, the puzzle was already a huge craze by 1880 and Loyd did not start claiming it was his until 1890. He claims, the real inventor was Noyes Palmer Chapman who originally showed his ’s’ son is supposedly responsible for taking the puzzle to friends the puzzle in 1874. Chapman Connecticut. In Connecticut, students from the American School for the Deaf started manufacturing the puzzle in 1879 (Fifteen Puzzle). It is hard to say which man invented the puzzle since neither received a patent. Chapman tried to get a patent for the 14-15 problem but was unable because there was a patent given to Ernest U. Kinsey for a similar but different problem in 1878 (Fifteen puzzle). Sam Loyd also tried to receive a patent but was denied for the 14-15 problem. In order to receive a patent, Sam Loyd had to present a working model of the puzzle. When the patent commissioner found out the puzzle was unsolvable he claimed no ’t have the patent (Carter). Even though the patent working model exists so you can commissioner knew the puzzle was impossible, most did not. Whether it was Sam Loyd, Noyes Chapman, or someone else, the puzzle swept the world. In Germany, deputies in the Reichstag were caught playing the game. In America, employers had to post signs explaining the puzzle “greater was not allowed to be played during business hours. And in France, it was deemed a ” (O’Conner). Later on, Loyd revealed the only way the puzzle scourge than alcohol or tobacco “by such skullduggery as turning the 6 and 9 blocks upside down” (Carter). was solvable is LaGrange 3 of 22 For the rest of his life Loyd continued to make puzzles which he distributed many different ways. He would publish them in different papers, sell them through the circus, or publish them himself. Later in life, he also became a performer with his son. He and his son had a skit where his son would appear to read his fathers mind. But, in reality, his son was a good ’Conner). In the 1890’s, Loyd wrote a column of puzzles for mime and Loyd a ventriloquist (O “Brooklyn Daily Eagle.” Then from 1904 until his death in 1911 he wrote a puzzle page for the “Woman’s Home Companion” (Gardner). Loyd died in his home at the age of 70 the ’Conner). In his obituary, published in the Times, it was said that he was “fantastic in (O mathematical science, and, had he devoted himself to making use of it, might have earned fame ” (O’Conner). But he didn’t as an investigator in the vast and political region of pure mathematics earn fame this way. He earned his fame as a puzzelist, leaving us with over 10,000 puzzles to ’Conner). After Loyd’s death his son organized a compilation of all his father’s puzzles solve (O ’s Cyclopedia of 5,000 Puzzles Tricks and Conundrums (Gardner). and created Sam Loyd ’s most famous mathematical puzzles along with a The following is a sample of Sam Loyd system for solving and a solution. (Some of the following problems have been edited for simplicities sake.) LaGrange 4 of 22 ’ Sam Loyd s Puzzles School of Sea Serpents One sea captain claimed that while he was becalmed off Coney Island he was surrounded “Three could not look from their by a school of sea serpents, many of which were blind. ” he reported, “and three could not look to larboard. Three could look to starboard blinkers, starboard, three to larboard, three would look both to starboard and larboard, while three had ” So it was duly entered on the logbook and duly sworn to both their optics out of commission. “there were eighteen serpents in sight.” But a couple of camera fiends who got a focus on that the school of monsters have developed their negatives in a way that negatives the whole story and reduces the number of serpents to the minimum of possibilities. Just how many serpents belonged to that school? Solution: The sea captain described 6 different categories with 3 serpents in each. ’t see starboard 1. can ’t see larboard 2. can 3. see starboard 4. see larboard 5. see starboard and larboard 6. completely blind But these categories, or sets, are not disjoint. The 3 serpents in category 6 also qualify for categories 1 and 2, while the 3 serpents in category 5 also qualify for categories 3 and 4. So, the actually minimum amount of serpents necessary is 6; 3 who can see in both directions and 3 completely blind. The Man with the Hoe It appears that for five dollars Hobbs and Nobbs agreed to plant a field of potatoes for Farmer Snobbs. Nobbs can drop a row of potatoes in forty minutes and cover them at the same rate of speed. Hobbs, on the other hand, can drop a row in only twenty minutes, but while he is covering two rows, Nobbs can cover three. Assuming that both men work steadily until the entire field is planted, each man doing his own dropping and covering, and further, assuming that the field consists of twelve rows, how should the five dollars be divided so that each man is paid in proportion to the work accomplished. Solution: If both men worked at exactly the same rate then each would drop and cover 6 out of twelve rows and they would split the five dollars evenly. As a baseline first check how long it would take each brother to finish 6 rows. Nobbs to drop (40min)(6 rows) = 240 min to cover (40 min)(6 rows) = 240 min 240 + 240 = 480 min. So it will take Nobbs 480 min. to complete 6 rows. Hobbs to drop (20 min)(6 rows) = 120 min to cover (60 min)(6 rows) = 360 min LaGrange 5 of 22 120 + 360 = 480 min. So it will take Hobbs 480 min. to complete 6 rows. ’t obvious from the initial problem, Hobbs and Nobbs are working at Therefore although it wasn the same rate over 6 rows so they should spilt the $5.00 evenly giving them each $2.50. The Three Brides Old Moneybags let it be known that he would endow his daughters with their weight in gold, so they were speedily suited with suitable suitors. All were married on the same day, and before weighing in partook of some exceedingly heavy wedding cake, which made the grooms very light-hearted. Collectively, the brides weighed three hundred and ninety-six pounds, but Nellie weighed ten pounds more than Kitty, and Minnie weighed ten pounds more than Nellie. One of the bridegrooms, John Brown, weighed just as much as his bride, while William Jones weighed half again as much as his bride, and Charles Robinson twice as much as his bride. The brides and grooms together weighed half a ton.
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