#08 Prisoners locked up
There are 40 prisoners in Hallaway women鈥檚 prison, each in their own numbered cell, and 40 prison officers. All the cell doors are open and it is time to lock up for the night. Unfortunately, the prison officers have been drinking. Near the cells, there is a bucket containing the numbers 1 to 40 on pieces of paper.
Each prison officer in turn does the following: Picks a number from the bucket (and doesn鈥檛 put it back); turns the key in the cell of the number on her paper and of all cells that are multiples of that number; then goes to bed.
Turning the key makes a locked cell unlocked and an unlocked cell locked.
The first officer picks number 12, so she turns the key (and locks) cells 12, 24 and 36. The next picks 8, and turns the key in 8, 16, 24 (again), 32 and 40. The other officers follow in turn, each with a different number. After all 40 officers have done the rounds, the prison director, knowing her staff were drunk, now visits each cell and turns the key.
Which prisoners are able to escape?
Answer next week
#07 Amveriric鈥檚 boat
Solution
If Benolin Chestikov pulls the rope horizontally by 1 metre, then the boat will not only reach the wall but it will start scraping up the side of the quay. This surprises most people.
Suppose the boat moves in by a distance x. The taut rope of length L is shortened by 1 metre to become L-1. The two shorter sides of the triangle must combine to be longer than the longest side (that is how triangles work). So x + L-1 > L, hence x-1 > 0 and x > 1.
Quick Quiz #08
1 In quantum physics, which rule named after a German scientist is used to extract a particle鈥檚 probable position from its wave function?
2 Painting flies onto the centre of urinals to direct men where to pee is an example of what vogue theory used to influence our behaviour?
3 Launched in 2009 and operational until October 2018, which NASA mission detected over 2600 planets in other solar systems?
4 Oncogenes are genes involved in promoting cellular growth whose malfunctioning can cause what condition?
5 The bee hummingbird, native to Cuba and the nearby Isla de la Juventud, holds what distinction?
Answers below
Quick Quiz #08
Answers
1 The Born rule, after Max Born
2 鈥淣udge鈥� theory
3 The Kepler space telescope
4 Cancer
5 They are the world鈥檚 smallest birds, averaging 5 to 6 centimetres in length
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