Challenge Answers 2001

There were a lot of excellent answers this year, with very little dividing the prizewinners from some of those who were awarded certificates. Well done to all who took part!

  1. Winnie broke one branch and bounced off four more in the first 105 feet; and no, I didn?t say whether he broke the others or not!
  2. a) 25 decrees. b) 16.67 decrees. c) 30 decrees.
  3. a) 30 seconds. b) 30 seconds. c) 60 seconds.
  4. In the first two weeks, player 8 can only pair with player 1. The rest can all be paired.
  5. In the third week, player 18 can only go with player 7. After that, player 2 can only go with player 14, and so on until player 15 must go with player 1.

    In the fourth week, player 18 could still only go with player 7; but if you carry on putting players together who have no choice of partners, you will find that some players cannot find square partners. So the first match is in week 4.

  6. Arr and Thur line up every 1 years. Cee lines up with these two only once in 23 times as long, which is every 34 years; and Klarc needs 29 times as long to line up with the other 3, making 1000 years. So they line up half way through the year 1000, but on the opposite side of their sun.
  7. It takes them twice as long to meet up on the same side they started, in 2001.

    You could say they had all completed a whole number of orbits in the year 29, as they have all done at least one orbit.

  8. The last day of this century will be a Thursday. As the centuries go by, the last days will fall on Tuesday, Sunday, Friday and back to Thursday again; and this cycle of four will repeat for ever, unless anyone is unwise enough to alter the calendar?
  9. The teacher must walk 16.5 metres.
  10. There are two single-colour cubes; two with a single square of one colour; four with exactly two squares of one colour; and two cubes with three of each, making ten in all.