BELINDAāS birthday present from Anne was a clock. Itās 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: āItās lovely ā but itās stopped. And however accurately I measure the position of its hour hand and its minute hand, I canāt find out when it stopped because I donāt know which hand is which. Itās one of two possible times, quite a bit apart; but I canāt tell which.
Anne: āAnd just where is its second hand pointing?ā
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Belinda: āI hadnāt thought of that ā¦ Almost straight up: it would have been pointing straight up less than half a second after the clock stopped ā if the clock hadnāt stopped (if you see what I mean).ā
Anne: āWell then, if the clock had been able to go on for that āless than half a secondā, and had then stopped with its second hand pointing straight up, it would have stopped when the time was H hours and M minutes.ā
What are the whole numbers H and M?
A Ā£10 book token will be awarded to the sender of the first correct answer opened on Thursday 14 December. The Editorās decision is final. Please send entries to Enigma 848, Ā鶹“«Ć½, Kingās 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) āOne point is exactly covered by its photographic imageā.
