#89 Sunday drivers
The single lane road around Lake Pittoresca is scenic, but a pain if you want to get somewhere fast. Four couples staying at the Hotel Hilberto plan a day trip to the lakeside village of Paradiso. The driver for each couple habitually takes life at a different speed. Mr Presto likes to go full throttle in his Porsche. Mme Vivace isn鈥檛 quite such a speedy driver. The Andantes prefer a leisurely drive, while inconsiderate Mr and Mrs Lento creep along in second gear.
If a car finds itself behind a slower car, there is no choice but to follow at the slower speed, and form a larger 鈥渃lump鈥� of cars (a clump can be any number, from one upwards).
After Sunday breakfast, all four couples set off and find they are in the only cars on the road. By the time they arrive at Paradiso, they are in two clumps. Later, they all head back in reverse order, and arrive at the hotel in three clumps. Mr Presto looks particularly stressed because he was barely able to put his foot down on the journey back. In which order did they set out?
Answer next week
#88 Rifling the draw
Solution
The chance that Kate has won is 1 in 7. Suppose they each shoot 25 times: 12/25 times Pat will hit and Kate will miss (= 4/5 x 3/5). Just 2/25 times Kate will hit and Pat will miss (= 1/5 x 2/5).
So when there is a single hit, the odds are 6:1 (or 6/7) that it is Pat鈥檚.
Quick quiz #81
1 NASA鈥檚 Dawn probe was the first spacecraft to visit and orbit what?
2 Which creatures build the world鈥檚 tallest animal-built structures?
3 Which condition makes people see visual objects as smaller than they are?
4 How many of the seven mathematical Millennium Prize Problems have been solved?
5 What gives chilli peppers their 鈥渂urn鈥�?
Answers
1 A dwarf planet. It arrived at Ceres, a dwarf planet in the asteroid belt between Mars and Jupiter, in March 2015
2 Termites. Their mounds can be up to 8 metres tall
3 Micropsia
4 Just one of the seven. The Poincare虂 conjecture was solved by Grigori Perelman in 2003
5 Capsaicin