BELINDA’S birthday present from Anne was a clock. It’s 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: “It’s lovely – but it’s stopped. And however accurately I measure the position of its hour hand and its minute hand, I can’t find out when it stopped because I don’t know which hand is which. It’s one of two possible times, quite a bit apart; but I can’t tell which.
Anne: “And just where is its second hand pointing?”
Belinda: “I hadn’t thought of that … Almost straight up: it would have been pointing straight up less than half a second after the clock stopped – if the clock hadn’t stopped (if you see what I mean).”
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Anne: “Well then, if the clock had been able to go on for that ‘less than half a second’, and had then stopped with its second hand pointing straight up, it would have stopped when the time was H hours and M minutes.”
What are the whole numbers H and M?
A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 14 December. The Editor’s decision is final. Please send entries to Enigma 848, Â鶹´«Ã½, King’s 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) “One point is exactly covered by its photographic image”.
