#62 Burger run
Three friends agree to drive from A to B via the shortest road route possible (driving down or right at all times). They are hungry, so also want to drive through a Big Burger restaurant, marked in red. They are arguing about how many shortest routes will pass through exactly one Big Burger. Xenia: “I reckon there are 10.” Yolanda: “I’d say more like 20.” Zara: “No you’re both wrong, I bet there’s more than 50.” Who is right, or closest to right?
Answer next week
61 Triple Jump
Solution
Let us call the mother’s age when the triplets were born M, so she had her (M + 1)th birthday before the triplets’ first birthday. The triplets’ age is X. We are looking for a time when either M + X = 3X (i.e. M = 2X) or when M + X + 1 = 3X (i.e. M + 1 = 2X). So whether M is even or odd, there will always be a value of X that works.
If the triplets were born on the mother’s Mth birthday, the ages will coincide when the mother is 1½M, which is only a whole number when M is even. In other words, if the triplets were born on the mother’s birthday, the chance of an age match is just 50 per cent. Overall, ignoring leap years, the chance that mother and triplet ages will match is (364/365) + (½ x 1/365) = 729/730, so about 99.9 per cent.
Quick quiz #54
1 “Who ordered that?” This was physicist Isidor Isaac Rabi’s response to the discovery of what particle in 1936?
2 Human babies are nidicolous. Why?
3 Bardeen, Brattain and Shockley are famous for what?
4 African-American chemist Alice Ball, who died in 1916 aged just 24, developed a successful treatment for which bacterial disease?
5 The epidemiological efforts of which doctor are recognised by a plaque on the side of an eponymous pub on Broadwick Street in Soho, London?
Answers on page 54
Quick quiz #54
Answers
1 The muon. A heavier version of the electron wasn’t on anyone’s menu
2 They are “nest-inhabiting”, dependent on their parents for survival
3 The invention of the transistor in 1948, for which they received the Nobel prize in physics in 1956
4 Leprosy; her story is told in a recent short film, The Ball Method
5 John Snow. He proved that the source of a cholera outbreak was the handle of a water pump just outside