Rutger's Website or the work at the
Laboratoire de Spectrometrie Physique in Grenoble.
Thanks to Rob Douglas for these questions.
1. Bethan opened her book and said "If I take the sum of the number of the page I am on with the number of the page on its right, I get 345". On which page is Bethan?
2. There are 15 players in a rugby union team. The average age of the players is 27 and 2/3 years. At half-time one of the players rushes off the pitch to write a book revealing that the captain is in fact a vampire bat. The average age of the remaining players is 28 years. How old is the author?
3. An island is populated by two types of student; Nice students, who always tell the truth, and Naughty students, who always lie.
(i) A stranger arrives at the island and meets two of its inhabitants, Claire and Lorna. Claire says "Both of us are Naughty". What types are Claire and Lorna?
(ii) It is well known that Naughty students drink lager whenever the opportunity presents itself, but Nice students never do. Matt, Gareth and Catherine were the only students present when all the cans of lager were drunk.
Matt says "Exactly one of us drank the lager".
Gareth says "Exactly two of us drank the lager".
Catherine says "All of us drank the lager".
Who drank the lager?
4. Let p be a positive whole number.
(i) Find a value of p such that all the values p, p + 2 and p + 4 are prime numbers.
(ii) Are there are other values of p for which p, p + 2 and p + 4 are prime numbers?
(Hint: if p + 1 is divisible by 3, what can you say about p + 4?)
5. Name three famous mathematicians.
Contact me: firstname.lastname@example.org
Simon's Bit Institute of Mathematical and Physical Sciences University of Wales Aberystwyth