The Independent Mind Olympics

With today's questions, our Mind Olympics come to an end. Remember, a set of correct answers to any single day's questions will qualify you for entry to the weekly draw from which one entrant will win pounds 100 worth of Waterstone's book vouchers. At the very end, all correct entries will go back into the hat for another chance to win the grand prize of a 21- volume Macmillan Family Encyclopaedia (worth pounds 525).

Questions set by Maslanka.

Illustration: Mike Harrington.

1 Show how an equilateral triangular biscuit can be cut by three straight sabre slashes into:

a) 4 identical pieces each with 3 sides; b) 3 identical pieces each having 4 sides; c) 3 identical pieces with 3 sides; d) 6 identical pieces with 3 sides each.

(Of course, you may only cut downwards in the vertical plane at right angles to the biscuit's surface.)

2 A fly walks across the top face of the biscuit starting at one edge (not a corner) and crossing to another. Not only that, but her path is the shortest that exactly bisects the area of the biscuit. Sketch her path.

3 Ten per cent of the inhabitants of Cacti Creek drink vodka, 20 per cent drink gin and 40 per cent drink beer. Two toughies drink all three but no-one drinks just two of these drinks. There are 61 characters so tough that they can stand up to social pressure and drink nothing at all. How many live in Cacti Creek?

4 The assistant at Gullible Gulch's General Stores has bored holes through an array of indutrial sized sugar cubes, removing a whole number of cubes to leave the same cross-shaped hole running through the cube, no matter which of the six faces you look at. What is the smallest number of cubes he could have removed?

5. R wl slkv blf szev vmqlbvw gsv Rmwvkvmwvmg Nrmw Lobnkrxh. Ru blf szev, kovzhv dirgv zg gsv vmw lu blfi zmhdvih: "R szev vmqlbvw gsv Rmwvkvmwvmg Nrmw Lobnkrxh". Yfg mlg rm xlwv, lu xlfihv! - Nzhozmpz

When you have solved all five puzzles, send the answers to: Mind Olympics (Final Day), the Independent, 1 Canada Square, Canary Wharf, London E14 5DL to arrive not later than 16 August.

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