#79 Marathon Relay
Ruritania is thrilled to be hosting The Continental Games, and the Queen has decreed that two of the country鈥檚 greatest athletes, Rimsky and Korsakov, will take it in turns to carry the torch on its 26.2-mile journey from the harbour to the stadium. For each leg of the journey, the athlete can choose to run for any distance between 1 and 3 miles before handing over the torch to the other. Of course, Rimsky and Korsakov both privately hope that they will be the one who runs the last leg and hence gets to light the Continental flame. A coin is flipped, and Rimsky correctly calls heads. Should he choose to run the first leg or should he give that honour to Korsakov?
Answer next week
#78 Farewell My Blubbery
Solution
The book has 153 pages. You can discover this by trial and error, but algebra offers a shortcut. The number of digits N needed to number a book with 100 pages is 192; with 101 pages it is 195. So, in general, if a book has ABC pages, N = 3(ABC) 鈥� 108. Try A = 1, which is the shortest possible book: 3 脳 (1BC) 鈥� 108 = CB1. If 3 脳 1BC 鈥� 108 ends in 1, then 3 脳 1BC ends in 9, so C must be 3. That means ABC = 1B3. The only value of B that works is 5, so there are 153 pages and these will take (as you may easily check) 351 digits to number.
Quick quiz #71
1 What other name was originally given to 51 Pegasi b, the first exoplanet orbiting a sun-like star to be discovered?
2 Who referred to mathematics as the 鈥渜ueen of the sciences鈥�?
3 Native to Australia and parts of Indonesia, Dicaeum hirundinaceum is a species of bird known for eating what plant?
4 In what year did German pharmacist Friedrich Sert眉rner first isolate morphine from opium?
5 The turquoise colour of many glacial lakes is caused by what substance?
Answers on page 55
Answers
1 Bellerophon, after a hero from Greek mythology known for capturing winged horse Pegasus
2 Carl Friedrich Gauss
3 Mistletoe. It is more commonly known as the mistletoebird or the mistletoe flowerpecker
4 1804
5 Rock flour, or glacial flour. This finely ground rock is produced by erosion. When particles of it are suspended in water, they reflect more blue and green light