#28 A well-timed nap
I keep an analogue clock by my bed. One afternoon, I had a nap. When I drifted off to sleep, the minute hand was pointing directly at one of the 12 numbers on the clock face, and the number of minutes past the hour was exactly the same as the angle (in degrees) between the hour and minute hands.
Later that day, when I woke up, I noticed the same was true again.
How long had I been asleep?
Answer next week
#27 The goblin game
Solution
To have the best chance of winning, Beth should place her goblin on square 6.
The average score on a die numbered 1 to 6 is 3.5, so in the long run, the chance of a counter landing on a square is going to be 1 in 3.5, which is about 29 per cent. This will be the chance of the counter landing on all of the high numbers on the board.
However, the odds are different in the early stages. Squares 1 to 6 can all be reached with a single roll of the die (a 16 per cent chance), but square 2 can also be reached by rolling 1 and 1, for example. By the time you get to square 6, there are numerous ways of reaching it, and the odds of landing on 6 work out to be about 36 per cent.
Squares 7 and above can only be reached by landing on one of squares 1 to 6 first, which lowers the odds. Indeed, the odds of landing on a number higher than 6 are always below 30 per cent.
Quick Quiz #27
1 Which is the longest of the cranial nerves emerging from the human brain, transmitting signals to and from organs including the heart, lungs and gut?
2 Four of the 12 cranial nerves deal with the workings of just one organ. Which?
3 The vestibulocochlear nerve transmits information from the ear to the brain concerning hearing and which other sense?
4 Which is the largest of all the cranial nerves, primarily concerned with transmitting sensory and motor information to and from the mouth and face?
5 Crosstalk between this nerve and the optic nerve is thought to cause what response to sudden exposure to sunlight, found in up to a quarter of people?
Answers below
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Quick Quiz #27
Answers
1 The vagus nerve
2 The eye
3 Balance
4 The trigeminal nerve
5 Sneezing