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!

- 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! - a)
**25**decrees. b)**16.67**decrees. c)**30**decrees. - a)
**30**seconds. b)**30**seconds. c)**60**seconds. - In the first two weeks, player
**8**can only pair with player 1. The rest can all be paired. - Arr and Thur line up every 1½ years. Cee lines up with these two only once in 23 times as long, which is every 34½ years; and Klarc needs 29 times as long to line up with the other 3, making 1000½ years. So they line up half way through the year
**1000**, but on the opposite side of their sun. - 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? - The teacher must walk
**16.5**metres. - 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.

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**.

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.