The GCHQ Puzzle Book: Perfect for anyone who likes a good headscratcher

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Eliminating those words whose 3 rd letter scores 3 in Scrabble (DEPTH, HOPED, JAMMY, LABEL, YACHT) leaves:

ALABAMA, ALASKA, ARIZONA, ARKANSAS, CALIFORN IA, CONN ECTICUT, MAIN E, MI CHIGAN, MINN ESOTA, NEW J ERSEY, NEW M EXICO, TENN ESSEE, WASHIN GTON, WEST VIRG INIA, WYOMIN G Animal/French: WEASEL/ BELLETTE, DEER/ CERF, CAMEL/ CHAMEAU, TOAD/ CRAPAUD, PENGUIN/ MANCHOT, REINDEER/ RENNE, SHARK/ REQUIN, MONKEY/ SINGE Film titles containing numbers. The number is used to determine the point size of the font for the remaining letters: a) WILLIAM SHAKESPEARE: The plays HAMLET, KING LEAR, THE TEMPEST, THE WINTER’S TALE, CORIOLANUS, TWELFTH NIGHT, TROILUS AND CRESSIDA, THE MERRY WIVES OF WINDSOR, THE MERCHANT OF VENICE, ANTONY AND CLEOPATRA with punctuation, spaces and letters in his name removed.TEN- homophones: TEN-COMMAND-MINCE (TEN COMMANDMENTS), TEN-ERR-REEF (TENERIFE), TEN-GALLOW-GNAT (TEN-GALLON HAT), TEN-NESSIE-WILLIAMS (TENNESSEE WILLIAMS), TEN-NIECE-ELBOW (TENNIS ELBOW) Can be preceded by a Prime Minister’s name: BLAIR WITCH, BROWN WINDSOR, GLADSTONE BAG, HEATHROW, MAJOR GENERAL, NORTH POLE, SALISBURY PLAIN, WELLINGTON BOOT

The 3 remaining words - linked by the word LINK - are (LINK) ARMS, CONNECTION (= LINK) and CHAIN (LINK). c) Three Men in a Boat (Jerome K Jerome) - There were four of us: George, and William Samuel Harris, and myself, and Montmorency. a) IMAGE. In all the others letters 1, 3 and 5 form a word: AGE, BIG, CAP, DRY, EAT, FED, GAS, HAT, JUT a) D - the sequence is the Roman Numeral letters contained in the names of the months in French: JAN VIER, FÈ VR IER, MARS, A VR IL, MA I, JU IN, JU ILLET, AOÛT, SEPTE MBRE, O CTOBRE, NO VE MBRE, DÈ CE MBREBATES/HE/2, BURROUGHS/ER/68, CLARKE/AC/89, GARDNER/ES/99, HEINLEIN/RA/88, JAMES/PD/46, LEWIS/CS/55, SHELLEY/PB/82, WELLS/HG/80, WOOLF/V/23 f) Anagrams of European countries: AIL+VAT=LATVIA, ANY+ROW=NORWAY, CAR+FEN=FRANCE, CUR+SPY=CYPRUS, END+SEW=SWEDEN, KEY+RUT=TURKEY, OLD+PAN=POLAND f) Denzel Washington - Captain Bennett Marco (from The Manchurian Candidate) - Frank Sinatra - Danny Ocean (from Ocean’s 11) - George Clooney - Batman - Michael Keaton - Beetlejuice The question then becomes: find such a sum that works for (at least) n=1, 2, 3, 4 and 5. For example: m) Madness = Chris Foreman, Carl Smyth, Daniel Woodgate, Graham McPherson, Lee Thompson, Mike Barson, Mark Bedford