Maslanka so­lu­tions

The Guardian Weekly - - Sport -

1 What tags on to what noun in an English sen­tence de­pends on where it is placed. Here it looks as if the res­i­dents en­gaged in an ex­tra­or­di­nary game of cha­rades im­i­tat­ing the be­hav­iour of rats be­fore com­ing clean and say­ing a rat in­fes­ta­tion is out of con­trol. And there again, you might con­sider it a defin­ing fea­ture of an in­fes­ta­tion that it’s al­ready out of con­trol. And do rats saunter? To­day’s cre­ative task: How can the sen­tence be re­formed so that it doesn’t con­jure up im­ages of the res­i­dents be­hav­ing like jaunty ro­dents? 2 If a2 + b2 + c2 = ab + bc + ca and we mul­ti­ply by 2 through­out we get 2a2 + 2b2 + 2c2 = 2ab + 2bc + 2ca. This can be rewrit­ten as (a– b) +(b – c) +(c – a) = 0. But the

2 2 2 quan­tity on the left can only be zero if each bracket is zero; whence a= b = c. That is – the tri­an­gle is equi­lat­eral. 3 We soon see that the top white tri­an­gle is sim­i­lar to the whole she­bang, and that its area is 1⁄4 of it; so what is left is 3⁄4 of it. Each tri­an­gle is ¼ of what re­mains; so we get for the black area: ( 1⁄4)(3⁄4) + 1⁄4(3⁄4) ( 3⁄4)(3⁄4) + ( 1⁄4)(3⁄4) +… = ( 1⁄4)(3⁄4)[ 1

5 +( 3⁄4) + ( 3⁄4) +…] = 3⁄7.

2 3 4 Imag­ine run­ning six tri­als on each urn. The first will con­trib­ute six 1s, the sec­ond, three 1s; and the third, two 1s. There­fore the chances the 1 came from urns 1, 2 and 3 are 6⁄11, 3⁄11 and 2⁄11, re­spec­tively. The chances of each urn given a 2 was with­drawn at ran­dom are 0, 3⁄5 and 2⁄5, re­spec­tively. Word­pool c) Same Dif­fer­ence CARTON, CAR­TOON Let­ters Play GRAVY (grey “V”) Miss­ing Links a) space/rocket/salad b) su­per/man/go c) Vene­tian/blind/date d) man/trap/door e) fresh/air/gui­tar f) for­bid/den/ounce

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