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Enigma: No. 826 Crescents

A RECTANGLE has sides &tgr; and 1/&tgr;, where &tgr; is the golden ratio &tgr; = ½ (√5+1). The circle circumscribing the rectangle is drawn, and semicircles are constructed on each of the four sides.

What is the total area of the four “crescent moons�, within the semi-circles, but outside the large circle?

A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 13 July. The Editors’ decision is final. Please send entries to Enigma 826, New Å®ÉúСÊÓÆµ, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 820 was Andrew Plant of Lymington in Hampshire.

Answer to Enigma 820

Hard cheese

No, you cannot clear the 6 squares in 1000 moves.