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University of Nebraska - Lincoln
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
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Sudoku, Marlene Grayer
Sudoku, Marlene Grayer
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Many people have a magazine, a crossword puzzle, a newspaper, or a book on hand to fill idle time. I, however, prefer to tease my mind with a book of Sudoku puzzles (pronounced sue‐dah‐coup), trying to figure out what number goes where while resisting the temptation to peek in the back at the answer to make sure I am on the right track. For those of you who are unaware of what Sudoku is, it is a highly popular number game whose notoriety may even surpass the crossword or word search puzzles. It can be found in popular newspapers such …
Sicherman Dice, Scott Johnsen
Sicherman Dice, Scott Johnsen
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Many different types of games involve the use of numbered dice. The most common type of die used is the standard six-sided die with the numbers one through six used on its six sides. What if there was another way of numbering a set of dice (using only positive integers) that would create the same probability outcomes as those of a standard set of dice? The February 1978 issue of Scientific American reports that George Sicherman discovered such a numbering (Broline, 1979). Sicherman discovered that two cubic die numbered 1-2-2-3-3-4 and 1-3-4-5-6-8 have the same sum probabilities as do the …
Amicable Pairs, Lexi Wichelt
Amicable Pairs, Lexi Wichelt
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The ancient Greeks are often credited with making many new discoveries in the area of mathematics. Euclid, Aristotle, and Pythagoras are three such famous Greek mathematicians. One of their discoveries was the idea of an amicable pair. An Amicable pair is a pair of two whole numbers, each of which is the sum of the proper whole number divisors of the other.
Palindromes, Stephanie Fuehrer
Palindromes, Stephanie Fuehrer
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
A palindrome is a word or phrase that reads the same forward and backward, such as the word “level” and the phrase “Madam, I’m Adam.” Numbers whose digits read the same forward and backward are also called palindromes, such as the numbers 22, 1234321, and 2002. Palindromic phrases can also occur in number form, for example the Universal day of Symmetry: 8:02 P.M. on February 20, 2002. If one were to look at the time on a twenty-four hour clock, it would read 20:02; the date can be read as the twentieth day of the second month, which also represents …
The Monty Hall Problem, Brian Johnson
The Monty Hall Problem, Brian Johnson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
In the game show "Let's Make a Deal", host Monty Hall would present a contestant with three doors. Behind one door is a car and behind the other two doors are goats. The contestant picks one door, after which Monty opens one of the other doors, showing a goat. Monty then offers the contestant the opportunity to keep the same door or switch to the other unopened door; the contestant will get to keep whatever is behind that door. Should the contestant switch?
Powers, Marci Ostmeyer
Powers, Marci Ostmeyer
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Powers, or exponents, give us a convenient, shorthand way to denote that a number is multiplied by itself a given number of times. The number being multiplied is called the base, and the number of times it appears in the product is the power.