#23: Circling the squares
Darts player Juan Andred has noticed that on a standard dartboard, there are some neighbouring pairs of numbers that add up to a square number. For example, 20 and 5 make 25, while 6 and 10 add up to 16. He has been wondering if he can come up with a new arrangement of the numbers 1 to 20 so that all neighbouring pairs add up to a square number. And he has nearly succeeded.
He has 20 at the top of the board, and every pair of neighbours adds to a square 鈥� with one exception. On his new board, 18 doesn鈥檛 form a square with its clockwise neighbour, which is 15, or with its anticlockwise neighbour.
What does Juan鈥檚 鈥渟quare鈥� dartboard look like?
Answer next week
#22 The 9-minute egg
Solution
The slow method for boiling an egg for 9 minutes: start the 7-minute and 4-minute egg timers. When the 4 runs out, flip it. When the 7 runs out, there is 1 minute left in the 4.
Put the egg on. When the 4 runs out (after 1 minute), flip it. When it runs out, flip it again to get 9 minutes. This means I won鈥檛 get my egg for 7+9=16 minutes.
Fast method: Start timers 7 and 4 and put the egg on. When 4 runs out (elapsed time 4 minutes), flip it. When 7 runs out (after 7 minutes) flip it. When 4 runs out again (elapsed time 8 minutes), flip the 7. When the 7 runs out (total 9 minutes), the egg is cooked. So I get my egg in 9 minutes.
Quick Quiz #22
1 The male sperm whale has the largest what of any animal on the planet?
2 Marie Curie (1903), Maria Goeppert Mayer (1963). What name and year come next?
3 Which element makes stainless steel stainless?
4 What were Tiangong-1 and Tiangong-2?
5 ARCT, GFST and MEDI are three examples of the 56 four-letter Longhurst codes used by earth scientists to refer to what?
Answers below
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Quick Quiz #22
Answers
1 Brain
2 Donna Strickland (2018). She was the third woman to win the Nobel prize in physics
3 Chromium, at a minimum of 10.5 per cent by mass
4 Chinese space stations, orbiting 2011-2018 and 2016-2019. The name means 鈥渉eavenly palace鈥�
5 Sea areas with distinctive biogeochemical conditions: here, the Atlantic Arctic, the Gulf Stream and the Mediterranean