Transcript PUZZLES
By Katie Dzerovych Jon Wood JB Henderson Mentor Professor Snapp Puzzle A game, toy, or problem designed to test ingenuity or knowledge. History The first puzzle found was an Egyptian document, the Rhind Mathematical Papyrus, that is over 3,600 years old There were 85 different puzzles in the papyrus One puzzle is: Seven houses contain seven cats. Each cat kills seven mice. Each mouse had eaten seven ears of grain. Each ear of grain would have produced seven hekats of wheat. What is the total of all of these? Archimedes invented a division of a square into 14 pieces leading to a game similar to Tangrams, Stomachion, involving making figures from the 14 pieces Quick Puzzles http://www.puzzles.com/puzzleplayground/OutOfGla ss/OutOfGlass.htm http://www.puzzles.com/puzzleplayground/CrazyCut /CrazyCut.htm http://www.puzzles.com/puzzleplayground/Counting TheSquares/CountingTheSquares.htm Tower of Hanoi Must transfer the tower of disks from one end peg to the other end peg The only rule is you cannot place a larger disk over a smaller disk Depending on the number of disks what is the least possible moves to make this work History of the Tower of Hanoi Created by French mathematician, Edouard Lucas, in 1883 Based on the legend of a Hindu temple where the puzzle was used as mental discipline for young priests The legend says that since the beginning of time the priests in the temple were giving a stack of 64 gold disks one each a little smaller than the one below it The priests were to transfer the 64 disks from one of the three poles to another, the only rule they had was that a larger disk could never be on top of a smaller disk The legend says that when they finish the temple will crumble and the world will end Tower of Hanoi Game http://www.speedyadverts.com/SAFlashGames/html/ game71.html Equation for Tower of Hanoi The number of moves grows exponentially with the number of disks used If n is the number of disks and M is the number of moves n M=2 -1 Homework The legend of Hanoi says that there were 64 disks the priests would have to move before the world would end, how long would it take the priests to move the disks if it took them one second a move? Works Cited O'Connor, J., and E. Robertson. "Mathematical Games and Recreations." May 1996. Web. 30 Nov. 2011. <http://www.gapsystem.org/~history/HistTopics/Mathematical_games.html>. Tower of Hanoi. Digital image. WTS. 2007. Web. 30 Nov. 2011. <http://www.wooden-toystore.com/Tower%20of%20Hanoi.asp>. Belluck, Pam. "Ancient Egyptians’ Mathematical Ingenuity, Written on Papyrus NYTimes.com." The New York Times - Breaking News, World News & Multimedia. 06 Dec. 2010. Web. 30 Nov. 2011. <http://www.nytimes.com/2010/12/07/science/07first.html?_r=1>. "LHS: Tower of Hanoi Facts." Lawrence Hall of Science. Web. 30 Nov. 2011. <http://lawrencehallofscience.org/java/tower/towerhistory.html>. Petković, Miodrag. Famous Puzzles of Great Mathematicians. Providence, RI: American Mathematical Society, 2009. http://www.tabbykat.com/Archimedes%20Square%20R.jpg http://www.tabbykat.com/Alexander%27s%20Star%20R.jpg http://www.tabbykat.com/Number%2015%20R.jpg http://en.wikipedia.org/wiki/Tangram http://www.sudoku.org.uk/ http://www.seriouspuzzles.com/i7134.asp