#69 Cutting the flag
I have a stripy flag laid out on my desk. The stripes are all of equal width, five of them in total. Because three of the five are blue, I know that three-fifths of the flag is blue. However, I take my scissors out and make two straight, angled cuts at both ends of the flag, one of them at about 45 degrees, the other almost straight across, leaving me with a stripy trapezium. What fraction of this trapezium is blue? Is it more, less or the same as the three-fifths for the original flag?
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#68 Diamonds
Solution
There were no diamonds in the box. Call the number of palaces P. There were P2 vases and P3 diamonds, of which Fidelio got P, leaving (P3 鈥� P) to share among the six daughters. Whatever value you choose for P, you鈥檒l find that P3 鈥� P is exactly divisible by 6, so all the remaining diamonds went to the daughters. Why? Because it is equivalent to P x (P+1) x (P-1), the product of three consecutive numbers, one of which must be divisible by 3, and at least one of the others divisible by 2, making the product divisible by 6.
Quick quiz #61
1 The European eel (Anguilla anguilla) is thought to breed in what shoreless sea, 6000 kilometres from its native waters?
2 If consumed raw, eel blood causes what toxic shock reaction in people?
3 China is estimated to have become the world鈥檚 largest eel consumer in 2007, although the numbers are slippery. What country did it overtake?
4 In what way is the name 鈥渆lectric eel鈥� misleading?
5 With what interpretation of quantum theory does Mark Oliver Everett, singer-songwriter of US rock band Eels, share a progenitor?
Answers below
Quick quiz #61
Answers
1 The Sargasso Sea in the Atlantic; many details of the eels鈥� spawning and migration remain mysterious, however
2 Anaphylaxis
3 Japan
4 The electric eel (Electrophorus electricus) isn鈥檛 actually an eel, but a knifefish; its electricity is genuine, with 80 per cent of its body given over to generating it
5 The many worlds interpretation; his father, Hugh Everett III, originated it in 1957