CHRISTMAS QUIZ

A small prize will be offered for the best solution emailed to A.Mann@gre.ac.uk by a Greenwich student before 5pm on Monday 18 January 2010 (deadline extended because of the bad weather). In the event of a tie, a winner will be chosen randomly. The judges' decision is final. For obvious reasons, the source of these questions won’t be revealed until afterwards. The quiz has seven questions.

Q1. Identify the mathematicians whose names are given below as anagrams. Accents and punctuation marks such as hyphens are omitted, and spellings are taken from the MacTutor History of Mathematics website
http://www-groups.dcs.st-and.ac.uk/~history/

a) ENRW
b) EIKLNV
c) EEKLPR
d) AAIIJNX
e) AHILMNOT
f) BEILLNORU
g) ACDEEHIMRS
h) AEMNNNNOUV
i) GKLMOOOORV
j) AAAEKKLOSVVY


Q2. What is the smallest two-digit integer?

Q3. Is 10^2010 + 1 prime? Justify your answer.

Q4. On average, how many times do you need to toss a fair coin before you have seen a run of an odd number of heads followed by a tail?

Q5.
Consider a chessboard – an 8x8 grid of squares in which each row and column is alternately black and white. You have 31 2x1 rectangles each the size of two adjacent squares of the chessboard. Remove the top left and bottom right corner squares. Is it possible to cover the 62 remaining squares with your 31 rectangles? Provide a solution or show that it can’t be done.

Q6. A, B and C are candidates in an election. There is an odd number of voters. The votes are counted and there is a three-way tie. As a tie-breaker the voters’ are asked for their second choices, and again there is a three-way tie. A suggests that, to break the tie, there be a two-way election between B and C, with the winner then facing A in another two-way election. Is this fair? And what is the probability that A would win the election if it were held in this way, assuming no voter changes their mind?

Q7. Here are two hidden messages. What do they say?

a) MERRY CHRISTMAS AND HAPPY NEW YEAR

b) AAAAA VHCTUMMLD