04spex1sam - Math 431 Sample First Evening Exam Room B239,...

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First Evening Exam Room B239, 6:15 - 7:15pm, February 23, 2004 M´arton Bal´azs 1. (45 points) “ Aoccdrnig to a rscheearch at an Elingsh uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae we do not raed ervey lteter by itslef but the wrod as a wlohe. Based on this research, let’s assume that an English word is uniquely determined by its frst and last letter, and the unordered set o± its other letters. Put it in another way, given an English word, changing the order o± the inner letters (and so leaving the frst and last letter fxed) cannot lead to a di²erent English word. Give then an upper bound on the number o± fve-letter English words, and compare it to the number o± all possible sequences o± length fve, composed o± any o± the 26 letters o± the alphabet. 1
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This note was uploaded on 08/11/2008 for the course MATH 431 taught by Professor Balazs during the Fall '05 term at Wisconsin.

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04spex1sam - Math 431 Sample First Evening Exam Room B239,...

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