BELINDA鈥橲 birthday present from Anne was a clock. It鈥檚 a very accurate clock, and one whose hands point, at any given time, exactly where they should point at that time. But the clock does have one drawback: by some whim of fashion its minute and hour hands are identical in appearance.
Belinda telephoned Anne: 鈥淚t鈥檚 lovely 鈥� but it鈥檚 stopped. And however accurately I measure the position of its hour hand and its minute hand, I can鈥檛 find out when it stopped because I don鈥檛 know which hand is which. It鈥檚 one of two possible times, quite a bit apart; but I can鈥檛 tell which.
Anne: 鈥淎nd just where is its second hand pointing?鈥�
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Belinda: 鈥淚 hadn鈥檛 thought of that 鈥� Almost straight up: it would have been pointing straight up less than half a second after the clock stopped 鈥� if the clock hadn鈥檛 stopped (if you see what I mean).鈥�
Anne: 鈥淲ell then, if the clock had been able to go on for that 鈥榣ess than half a second鈥�, and had then stopped with its second hand pointing straight up, it would have stopped when the time was H hours and M minutes.鈥�
What are the whole numbers H and M?
A 拢10 book token will be awarded to the sender of the first correct answer opened on Thursday 14 December. The Editor鈥檚 decision is final. Please send entries to Enigma 848, New 杏吧原创, King鈥檚 Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 842 was Anna Brady of Herne Hill, London.
Answer to Enigma 842
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(i) Yes; (ii) X; (iii) 鈥淥ne point is exactly covered by its photographic image鈥�.