I鈥檓 on holiday in the lovely country of Philitaly, and planning to send plenty of postcards because postage is very cheap. But the country only allows up to three stamps on any letter.
Can you tell me which three denominations of stamps would allow me to cover any cost of postage from 1 cent to 15 cents inclusive?
And which four stamp denominations would allow all values from 1 to 24 cents?
Answer next week
Solution
We are told that one of 18鈥檚 neighbours is 15. The other neighbour can鈥檛 be 7 (because 18+7=25), so 7 must appear somewhere else. The neighbours of 7 can only be 2 and 9. Working outwards, this forces a chain that goes: 11-14-2-7-9-16-20-5-4-12-13-311鈥檚 other neighbour can only be 5 if it must make a square, but 5 is already in the chain, so 11 must be the other neighbour of 18.15鈥檚 other neighbour could be 1 or 10. If 1, then the chain would be 15-1-8-17-19-6-10-X. But if 10, then it would be 15-10-6-19-17-8-1-3, which completes the loop, like this:
Quick Quiz #23
1 The EPR thought experiment, proposed by Albert Einstein, Boris Podolsky and Nathan Rosen in 1935, introduced the world to which phenomenon?
2 The 10,000-year-old archaeological site G枚bekli Tepe lies in the south-east of which country?
3 What name is given to solids whose underlying atomic structure is ordered, but doesn鈥檛 repeat regularly?
4 快猫短视频s studying which bird in 2016 found they spent up to 10 months in the air without ever landing?
5 Dialogue Concerning the Two Chief World Systems 鈥� which systems, and written by whom?
Answers below
Quick Quiz #23
Answers
1 Quantum entanglement 鈥� or 鈥渟pooky action at a distance鈥�, in Einstein鈥檚 disparaging phrase
2 Turkey. Its monumental structures raise the question of which came first, civilisation or religion
3 Quasicrystals. Long considered impossible, the first natural example was identified in 2009
4 The common swift
5 Wrote Galileo, heretically, of the Ptolemaic and Copernican cosmological systems
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Article amended on 21 October 2019
鈥� There turns out to be at least one other rearrangement of a dartboard in which each neighbouring pair adds up to a square number: 20, 18, 15, 10, 6, 19, 17, 8, 1, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9, 16.