Maslanka puz­zles

The Guardian Weekly - - Diversions -

1 “Fifth! Jewellery! A quar­ter! Bur­glary – you nod­dle-headed Ne­an­derthal!” This was the sub­stance of the yells that punc­tu­ated the blows of a sledge­ham­mer as it re­duced a nifty­look­ing DAB ra­dio to bits. What sole­cisms was Pedan­ti­cus re­fer­ring to?

2 “Squar­ing a num­ber makes it big­ger,” pro­nounced Andy as he pored over a ta­ble of squares. But Candy wasn’t so sure. “It de­pends what you mean by a ‘num­ber’,” she replied. Andy sighed: “Clearly I am re­fer­ring to what you pedants call ‘real num­bers’; you know, stuff like 17, 0, 11/3, √ 2 and 666.” Show that Andy is wrong, and find the range of num­bers which grow smaller on squar­ing.

3 As the pop­u­la­tion of the coun­try shoots up, de­vel­op­ers are twist­ing the arms of the coun­cils to free space to pack full of poky lit­tle houses far too small for civilised oc­cu­pa­tion but cost­ing what a de­cent house once cost. I caught sight of this mea­gre lit­tle el­e­va­tion at the ar­chi­tect’s. The shape con­sists of a tri­an­gle on top of a rec­tan­gle. The walls and both slant sides of the roof are of unit length and the area of the gable is g. The an­gle at the top is 120°. What is the area of the rec­tan­gle? Twit­ter: @ChrisMaslanka

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