#09 The cake and the candles
Lady Frederica von Battenberg has baked a long, thin rectangular cake for her daughter Victoria. She has picked two random points on the top of the cake on which she has placed two candles.
She hands the cake knife to Victoria, who now proceeds to pick a random point along the length of the cake, and cuts across the cake at that point.
Now that the cake has been cut in two, what is the chance that both pieces of cake have a candle on them?
Answer next week
#08 Prisoners locked up
Solution
All the prisoners in cells that are square numbers can escape.
Consider cell 14, for example. It is visited by those prison officers whose numbers divide into 14, namely 1, 2, 7 and 14 鈥� otherwise known as the factors of 14. The factors can be grouped into pairs that multiply together to make 14: 1 and 14, 2 and 7. Since there is an even number of factors, the doors will end up open, the same state they started in.
Square numbers, however, have an odd number of factors. For example the factors of 16 are 1 and 16, 2 and 8, and then 4 (the square root). These cells therefore end up locked.
The prison director now turns every lock, meaning that the square numbered cells are open and all of the others are locked.
Quick Quiz #09
1 Curium, named after Marie Curie, is one of two chemical elements named after a woman. What is the other?
2 Shortly after the discovery of argon, the French chemist Paul-茅mile Lecoq de Boisbaudran proposed the existence of which new group of elements?
3 Too reactive to occur freely in nature, which fuming red substance is the only non-metal to be liquid at room temperature?
4 The Mountain Pass mine in California once held a near-monopoly on the world鈥檚 supply of which technologically crucial elements?
5 What capital connection do the chemical elements hafnium, holmium and lutetium share?
Answers below
Quick Quiz #09
Answers
1 Meitnerium, named after the Austrian-Swedish pioneer of nuclear fission, Lise Meitner
2 The noble gases
3 Bromine
4 Rare earth metals
5 They are named after Latin titles of European capitals: Copenhagen (Hafnia), Stockholm (Holmia) and Paris (Lutetia)
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