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Summer puzzles

Have a go at these puzzles, adequate for your holidays!

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puzzles Flickr user Marie Andersson, licence CC BY-NC-SA 2.0.

This week, we have some puzzles for you!

The Solstice Puzzle

The part of the Earth enclosed between the Tropic of Cancer (23.44° North of the Equator) and the Tropic of Capricorn (23.44° South of the Equator) might have the Sun directly overhead at some point during the year. What fraction of the surface of the Earth will never have the Sun directly overhead?

Summer Solstice Sunset Flickr user Jason, licence CC BY-NC-SA 2.0.

 

La Scuadra di Milano

Two football players are located in a specific location on a football pitch. Where should a third player be located such that the triangle that is formed between them has a right angle?

DSC_6440_free_crop_fix_soccer_KIPP Flickr user Innovation_School, licence CC BY-NC-SA 2.0.

 

Too many airports

A country has $N > 6$ airports and you can take a flight between any pair of airports. Suppose that you want a return ticket from airport A to airport B, going via at most two other airports on each part of the journey. How many combinations of airports are there such that no connecting airport is visited more than once throughout the whole trip?

Airport “Tunoshna” Yaroslavl city Flickr user Aleksander Markin, licence CC BY-NC-SA 2.0.

If you enjoyed these puzzles, you should try our crossnumber! You have until 22 July 2017 to submit an answer. Correct answers might win prizes!

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