Challenge 2002 Answers

If you have any questions or comments about this year's Challenge, please email me at P.M.Strickland@livjm.ac.uk.
  1. Good to Talk: After 13 minutes "Chatterbox" becomes the best option.
  2. Fly by Night: If you buy your nets in fives, they will cost £19.98; but if you buy them singly, you only need pay £19.90!
  3. A long way to go: The total length is about 1.75 km, which is more than a mile!
  4. Vital statistics: Out of a group of 100 containing 50 Quargs and 50 Xtrangs, you can expect that 100/20 = 5 are able to nixify. As four times as many Quargs as Xtrangs have this power, you would expect one of these to be an Xtrang, and the other four to be Quargs. So the answer is four.
  5. Mind the Gap: At 30mph, you can fit 450/7, or roughly 64, cars into a mile of road. Multiplying by 30 shows that 1920 cars pass per hour. If you do the same calculation for the other speeds you will find this is the most cars that can pass per hour, so the answer is 30mph.
  6. What a Carry On! On the five pointed star, the players end up running backwards after turning through 180°. So the angle turned at each corner is 180°/5 = 36°.

  7. There are two sorts of regular 7-pointed stars. Running round the first of these will involve turning through 540°, which is roughly 77° at each corner; running round the second will turn the player through 180°, which is nearly 26° at each corner.

    There is only one regular 8-pointed star; but as it has an even number of edges, the players end up pointing the same way they started, after turning through 360°. Each corner has an angle of 45°.
     

  8. Painting by Numbers. For the tetrahedron, only one face can have a given colour; for the cube, there can be two faces the same, four for the octahedron and three for the dodecahedron. Surprisingly, eight faces can be coloured in the same way for an icosahedron, as with the black faces in the picture below; the remaining faces can be coloured using two other colours.