#42 The card conundrum
Carl scribbled down an equation that contained only numbers and the letter x on a scrap of paper and left it on a table.
Bob found the card and realised that this was just a straightforward algebra problem. “I’ve found the solution,” he announced a minute later, dropping the card back on the table and leaving the room. Amy overheard him, walked over and picked up the card. After a while she announced: “That’s strange, I’ve found TWO solutions.”
Even stranger, Amy’s solutions were both different to Bob’s. What were the solutions that Bob and Amy found?
Answer next week
#41 Hen party dorm
Solution
There was a 50 per cent chance that Janice would end up in her own bed. Anyone who got back and found their bed was occupied, picked another bed at random. Two of the unoccupied beds were Amy’s and Janice’s, and there was an equal chance of picking either one. If Amy’s bed was taken at any point, then Janice would get her own bed, otherwise Janice would end up missing out.
So the answer to what sounds like a difficult probability problem is simply a half. The ninth friend, Iona, would get her bed if somebody picked either Amy’s or Janice’s bed before Iona got back. Since there were more ways in which Iona could end up with her own bed, she was more likely to get her bed than Janice.
Quick quiz #35
1 Twilight is divided into three phases: civil twilight, where there is enough light to see what you are doing; nautical twilight, where brighter stars are visible for navigation; and a third phase, known as what?
2 Adding roads to a congested traffic network can raise overall journey times. Whose paradox, first expressed in 1968, is this?
3 Oddly sturdy bone structures in 375-million-year-old Tiktaalik fossils found in Arctic Canada seem to show what giant evolutionary leap?
4 In what situation would you be grateful for the enzyme thrombin polymerising fibrinogen to form fibrin?
5 What happened to 67P/Churyumov–Gerasimenko on 12 November 2014?
Answers below
Quick Quiz #35
Answers
1 Astronomical twilight, where the sun is between 12 and 18 degrees below the horizon and residual light may still impede observations
2 Braess’s paradox, named after the German mathematician Dietrich Braess
3 Fish growing four legs and preparing to walk on land
4 In the event of a cut to your skin; this describes the process of a blood clot forming
5 It became the first comet to be landed on by a human probe, when the Philae lander from the European Space Agency’s Rosetta mission touched down