87 PROSPECT APRIL 2014 Enigmas & puzzles Fruit BalancingFinding act The generalist by Didymus 1 2 3 4 5 6 7 11 8 9 10 Barry R Clarke 12 A 13 D 14 15 16 B 17 18 19 20 21 23 C 22 24 25 At Jack the grocer’s market stall, of are At Jack the grocer's market stall, a system of scalesa ofsystem negligible weight balanced of by three different types of fruit:are strawberries, pears, by and three pineapples. scales negligible weight balanced Which missing single fruit are at positions A, B, C, and D? different types of fruit: strawberries, pears, and Solution: A strawberry (S) is at A, a pear (R) is at B, a pineapple (P) at C, and a pear at D. pineapples. On the bottom middle scales, taking moments (weight times distance), 2xR=1xP, so P=2R.Which On the bottom right fruits arrangement, so A, S=3R. middle left missing are 1xS=1xP+1xR, at positions B, On C, the and scales, 2xB+2x3R=1x3R+1xR+1xC+1x2R. So 2B=C. This means B=R (pear) and C=2R D? There of now fruit each position. (pineapple). For is theone top piece scales we addatthe weights of the lower scales to get 26 27 28 29 30 31 32 33 moments. For the top left (including the B and C weights) we have 3xR+2xA+1x2R+1x13R (3 pears, 2 pineapples, 2 strawberries). For the top right, we have 1xR+2x2R+2x8R+3xD. Last month’s solution Equating these gives 2A=3R+3D, so A=3R (strawberry) and D=R (pear). 34 35 37 36 38 39 41 42 40 43 44 45 ACROSS 11Influential 1950s and 1960s series of reading books for schoolchildren (5,3,4) 12 Feverish (8) 13Seafood dressing of mayonnaise and tomato sauce (5,4) 14At first sight, in Italian (1,5,5) 15I suppose I might! (3,2,4) 17Brothers Grimm story, a 1990 film starring Björk or a two-act opera by Philip Glass (7,4) 19Close-fitting headwear worn by a bride (6,3) 21Covered with cheese or breadcrumbs (2,6) 25One who advocates secession from a group (13) 26Sets of eight items (6) 28RC prayers for special occasions, spread over nine days (6) 30It neutralises radioactivity or poisons (13) 33… de Paris, the public executioner of France (8) 34A spirant, such as f or s (9) 37Black Country town, “Woden’s open land” (11) 39Fifth century British ruler who 46 married Rowena, Hengist’s daughter (9) 41Smooth glossy texture for a decorator (5,6) 42Founding father of the Republic of China (3,3-3) 45Rodin, Bernini or Brancusi, e.g. (8) 46Lightning flashes associated with Titfield? (12) DOWN 1Malaysian state on Borneo, capital Kuching (7) 2The connecting bands holding insects’ forewings and hindwings together (10) 3Achillea millefolium (6) 4Thomas …, whose Totentanz was premiered at the 2013 Proms (4) 5Where the Matchgirls’ Strike of 1888 at Bryant and May’s factory took place (3) 6Purchases a bargain—or trifles as Autolycus would (5,2) 7Of pharmaceutical products, available without prescription (9) 8Layperson dedicated to a monastic or religious life (6) 9An attendant (10) The original water level was 7/10 of the tank height. Let the original fraction of the tank height be x, the inside area of the base of the tank be A, and the area of an upright brick in contact with the inside tank base be B. The area of water in contact with the bottom of the tank when a single brick is introduced is (A – B), and becomes (A – 2B) for two bricks. So since the water volume is the same when no bricks, one brick, and two bricks are in the tank we have Ax = (A – B)4/5 = (A – 2B)14/15. This gives A = 8B and x = 7/10. How to enter 10Final Quartet (6,7) 16Republic whose unicameral parliament is the Saeima (6) 18Scottish lord, husband of Mary Queen of Scots, murdered in 1567 (7) 20Territory under the jurisdiction of a Muslim leader (7) 22Metal ring lining an eyelet (7) 23Hardline policing stance in response to undesirable conduct (4,9) 24Artist whose works are displayed in “his” gallery at Salford Quays (1,1,5) 27Plaster for exterior walls or used to make architectural mouldings (6) 29“The bare necessities”! (10) 31Half of “satnav” in full (10) 32Main ferry terminal on Mull (9) 35Small private rooms (7) 36Old French land measures varying from 1�/� to �/� acres (7) 38A defensive back in American and Canadian football (6) 40A nozzle for a blast of air (6) 43In heraldry, wavy (4) 44(He) kills, in France (3) Last month’s solutions Across: 1 Zinfandel 6 Albert Camus 12 Parroting 13 Ivan Lendl 14 Avens 15 Alectryon 16 TV dinners 17 Sal 18 Notts Forest 19 Esclandre 20 Lake District 22 Beliefs 25 Salzgitter 28 Fenestella 30 Tiercel 31 Quetzalcoatl 36 Orchestre 37 Street elbow 39 Sic 40 Araignées 41 Stonewall 42 Ibiza 43 Nuku’alofa 44 Maskarade 45 Sweet orange 46 Assiduous Down: 1 Zuppa inglese 2 Norbert 3 Amortised 4 Dairy cows 5 Loganberries 6 Alpenstock 7 Bristles 8 Rhabdocoele 9 Colonialist 10 Manuel de Falla 11 Salesmen 21 Killiecrankie 23 Western Samoa 24 Paul’s walkers 26 Gormenghast 27 Theatre-goer 29 Que sçais-je? 32 Anemopsis 33 Cleveland 34 Johannes 35 Messiaen 38 Bravado The generalist prize The winner receives a copy of Letters of Note (Canongate, £30), a collection of more than 100 letters compiled by Shaun Usher, from Leonardo da Vinci’s job application, to Gandhi’s appeal for calm to Hitler, to Virginia Woolf ’s suicide letter. Including photos of the original letters, this book has been hugely popular. “Funny, tragic, brilliantly incisive, historic, lyrical... My book of the year. You will never tire of it”—Stephen Fry Enigmas & puzzles prize One winner receives a copy of Everyday Calculus: Discovering the Hidden Math All around Us by Oscar E Fernandez (Princeton, £16.95). Fernandez, assistant professor of mathematics at Wellesley College, reveals the hidden calculus behind everyday events—how hot coffee cools down, for example—and explores how we can use it to solve common problems. Rules Send your solution to [email protected] or Crossword/Enigmas, Prospect, 5th Floor, 23 Savile Row, London W1S 2ET. Include your email and postal address. All entries must be received by 11th April. Winners will be announced in our May issue. Last month’s winners The generalist: Clarence Pardoe, France Enigmas & puzzles: Rebecca Hanson, Cumbria Download a PDF of this page at www.prospectmagazine.co.uk