# Maslanka solutions

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 The chances of each urn given a 2 was withdrawn at random are 0, 3⁄5 and 2⁄5, respectively.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