# Summer puzzles

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.

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!

• ### Christmas puzzles: the solutions

We reveal the solutions to our Christmas puzzles!
• ### Christmas puzzle #3: Colouring by numbers

Puzzle #3 in our 2020 Christmas puzzle series
• ### Christmas puzzle #2: A Christmas nonogram

Puzzle #2 in our 2020 Christmas puzzle series
• ### Christmas puzzle #1: Christmas tree sudoku

Puzzle #1 in our 2020 Christmas puzzle series
• ### Rewatch the Issue 12 virtual launch event

Now available to catch up on YouTube
• ### Read Issue 12 now!

Independent Sage's Christina Pagel, hyperbolic mindfulness and make-your-own Markov tweet feature in our latest edition. Plus all your favourite puzzles & columns.