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The Answers

The Answers. Challenge ‘ 13. Black Magic.

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The Answers

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  1. The Answers Challenge ‘13

  2. Black Magic Egrun, the wild green witch of the Wirral, roars along its lanes at nightfall astride her wood-burning Kawasaki broomstick. One night, she rides from the former Cadbury’s factory in Moreton at midnight to visit the Wizard of Oswestry for a short spell. But when she gets to Chester, her faithful catnav, Subordinate Claws, reminds her that she has forgotten the chocolate. So she goes all the way back for it. It’s 20 miles from Moreton to Chester and 30 miles from Chester to Oswestry. Egrun always rides at a steady 120mph and nothing EVER gets in her way. At what time does she arrive in Oswestry?

  3. Black Magic Moreton 00:10 00:20 00:45 Chester Oswestry

  4. Pick and Mix Robert and Miriam need chocolates as prizes for a quiz: they decide on four bags of Revels, five Mars Bars and five Twix Bars. However, they don’t coordinate their shopping! Robert buys three bags of Revels, two Mars Bars and four Twix Bars for £5.85; Miriam separately purchases two bags of Revels, four Mars Bars and three Twix Bars for £5.60. They return the excess goodies to the shop, receiving £2.60 back. How much does each item cost?

  5. Pick and Mix This is best considered as three simultaneous equations: 3r + 2m + 4t = 585 [1] 2r + 4m + 3t = 560 [2] r + m + 2t = 260 [3] 2r + 2m +4t = 520 [4] = [3] × 2 r = 65[5] = [1] – [4]

  6. Pick and Mix Sub into [3] → m + 2t = 195 [6] sub into [2] → 4m + 3t = 430 [7] 4m + 8t =780 [8] = [6] × 4 5t = 350, so t = 70 [8] – [7] Sub r = 65 and t = 70 into [3] → m = 55 So Revels cost 65p, Twix cost 70p, Mars cost 55p

  7. Fred and George are to share a chocolate bar made up of an 8 by 6-square rectangular array. The top-left & top-right squares each contain a visible nut. They take it in turns, starting with Fred, to snap the chocolate into 2 pieces along a line between 2 rows or 2 columns, & then eat 1 of the 2 pieces. Neither Fred nor George wants a nut. Which person can guarantee that they won’t get the nut? Is this true for any size of bar? Who’ll Nut?

  8. Who’ll Nut?

  9. All Because The Ladies Love… Ingrid, Jean, Karen, Philippa and Shirley are sharing a box of chocolates. There are 5 chocolates left in the box: a Coffee Cream, an Orange Fondant, a Hazelnut Praline, a Toffee Crunch & a Nougat Supreme. They agree to have one chocolate each. Ingrid likes only Orange Fondants and Toffee Crunches; Philippa likes only Orange Fondants and Hazelnut Pralines; Jean and Shirley both like Coffee Creams, Hazelnut Pralines and Nougat Supremes; and Karen likes only Toffee Crunches and Nougat Supremes. List all the possible ways that the chocolates can be shared such that all of the ladies get one that they like?

  10. All Because The Ladies Love…

  11. The Trouble With Truffles There are 9 chocolates in a selection box: 3 white, 3 milk & 3 dark chocolates. There are 3 soft centres, 3 truffles & 3 pralines. Each chocolate is different. Using the clues below, arrange the chocolates in a 3 x 3 grid: The 3 truffles are in the central column; there is 1 of each colour in each column; there are no 2 soft centres are next to each other horizontally, vertically or diagonally; the same applies for the pralines; the white praline is in the bottom-right corner; the 3 whites are arranged along a diagonal line; there are no dark chocolates in the bottom row.

  12. The Trouble With Truffles The 3 truffles are in the central column; there is 1 of each colour in each column; there are no 2 soft centres are next to each other horizontally, vertically or diagonally; the same applies for the pralines; the white praline is in the bottom-right corner; the 3 whites are arranged along a diagonal line; there are no dark chocolates in the bottom row. S S T T P P P P T T S S S S T T P

  13. Be Twix and Between How many different ways can you arrange the letters of the word CHOCOLATE? There are 9 choices for the first letter, 8 for the second and so on. This gives us 9×8×7×6×5×4×3×2×1 = 362,880 = 9! However there are 2 ‘C’s and 2 ‘O’s, so we need to halve this number for each of them 362,880 ÷ 2 ÷ 2 = 90,720

  14. Chocolate Brownies Seven Brownies and three Leaders have baked 35 chocolate cupcakes and eaten them all. One Leader ate one cupcake, another Leader ate two cupcakes, and the third Leader ate three cupcakes. Only whole cupcakes may be eaten. Show that at least one (greedy) Brownie ate at least 5 cupcakes.

  15. Chocolate Brownies 1 Cupcake 3 Cupcakes 6 Cupcakes 13 Cupcakes 20 Cupcakes 27 Cupcakes 34 Cupcakes 35 Cupcakes

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