A Christmas maths quiz

A small prize will be awarded for the best answers submitted to A.Mann@gre.ac.uk by a University of Greenwich maths undergraduate by midnight on Sunday 4 January 2009. The rest of you are doing it for fun only!

Q1. Identify the mathematicians whose names have been shuffled so that the letters are in alphabetical order. (Some are easier than others!) As extra help, they are given in chronological order. 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) AEHLST
b) AAHIPTY
c) AAHKMYY
d) DEE
e) AEFMRT
f) AHILLOPT
g) EELRU
h) ADEGMNOR
i) AAAJMNNRU
j) ACDIR

As a tie-break, can you suggest a candidate for the mathematician with the longest name in which the letters are in alphabetical order, so that (like one of the above) they would appear unchanged if their name were included in the above list? (My best so far is five letters long.)

Q2. Can you find English words containing the following letters consecutively?
a) WKW
b) HIPE
c) ZV
d) HQ
e) NSW

Q3. Which of the United States is closest to Africa?

Q4. There are several different time zones in the United States. New York on the east coast is normally three hours ahead of Los Angeles on the west coast. A phone call is made from an East Coast state to a West Coast state and it is the same time at both ends. How can this be?

Q5. There are 100 lightbulbs and switches, numbered 1 – 100, and 100 students. Initially each bulb is off. The first student switches on every light. The second then switches off every second light. The third student now changes the state of every third bulb, so 3, 9, 15,… are switched off and 6, 12, 18, … are switched back on. The fourth student changes the state of every fourth bulb, and so on. After the 100th student has done this, which bulbs are left on?

Q6. On average, how many times would you have to roll a fair die before all six numbers have appeared?

Q7. Sasha and Siobhan are in the same class. They look alike, have the same birthday, were born in the same year, and have the same parents. Yet they are not twins. Can you explain this?

Q8. Let n be a natural number. Show that there is an integer (non-zero) multiple of n which (in base 10) contains only 1s and 0s.

Q9. Can you decipher this message?

SZKKBSLORWZBGLBLFZOO

Q10. And can you decipher this one?

JUTZ JU ZNOY WAOF ATZOR EUA NGBK JUTK GRR EUAX IUAXYKCUXQ!