#50 Crossing the river
Petal is on her way to a country fair, to sell some vintage kitchenware belonging to her good friend Gretel. As she walks along the River Biddle admiring the view, Petal trips on a pair of oars left carelessly on the bank. A valuable wrought-iron kettle flies out of her hand and lands on one of the river鈥檚 many marshy islands.
From the river bank to the island is 3 metres directly across, and though the oars are sturdy enough to walk on, they are just short of reaching over the water.
How can Petal reach the island with the paddles and save Gretel鈥檚 metal kettle from its muddy peril?
Answer next week
#49 The tree in the snow globe
Solution
The tree can move 8 centimetres from the centre. Viewed side-on, so the snow globe appears as a semicircle, imagine moving the tree as far as it can go. Line b, from the centre of the base of the globe to the top of the tree, is the radius of the semicircle: 10cm. The height of the tree and the distance it has moved form the other two sides of a right-angled triangle, so we can use Pythagoras鈥� theorem to find the distance.
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Quick quiz #42
1 What objects are classified by position on a Hertzsprung-Russell diagram?
2 Tarsiers, tiny primates in South-East Asian jungles, are notable for having relatively enormous what?
3 Paris, Marrakesh, Bonn, Katowice, Madrid鈥� what city is next in this sequence?
4 A German scholar outlined 23 great unsolved problems of mathematics in a famous address at the Sorbonne in Paris in 1900. Who was he?
5 Which of his problems, involving the distribution of prime numbers, remained sufficiently great and unsolved a century later to be one of seven 鈥淢illennium Problems鈥� announced by the Clay Mathematics Institute?
Answers below
Quick quiz #42
Answers
1 Stars, placed on two axes according to their luminosity or magnitude, and their temperature or colour
2 Eyes. The only entirely carnivorous primates, they are nocturnal hunters with eyes that, at around 1.5 cm in diameter, are as big as their brains.
3 Glasgow. It will hold the 2020 annual UN climate change conference
4 David Hilbert
5 The Riemann hypothesis