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IT'S MAY and it's a holiday and time to turn away from ugly problems to more aesthetic questions. First, let's clear up some of last week's outstanding puzzles. Three flies swim in a straight line away from a common starting point in a bowl of soup. How can the starting point be found?

On the assumption that they all swim at the same speed, their position at any given moment must lie on a circle centred on their starting point. All three must be the same distance from its centre, which must be on a line at right angles to the line joining any pair of flies. Do this for two pairs of flies and where the two lines cross, there's the starting point (C in Fig 1).

Three legs good, four legs not so good. Under what wobbly circumstances? Why?

This had to do with chairs and tripods. Three-legged chairs are less wobbly than those with four. This is because a tripod or three-legged stool can have all its legs brought into contact with an uneven floor in a way a four-legged one in general cannot - hence the frequent need to put something under a leg of a four-legged table.

COSY IGLOO turns out to be an anagram of SOCIOLOGY, a hybrid word with its first half of Latin, its second of Greek derivation. I NOTE EVILS is an anagram of another such hybrid, found in the home. Can you spot what it is?

Too easy? In that case, of which seasonal refrain is NIGHTMARE SYNAGOGUE WHITENER an anagram? (4, 2, 2, 9, 4, 2, 3) and of what word is the third- to-last word a corruption? And, while we're on the subject, what is so special about the following: in one of the Bard's best-thought-of tragedies, our insistent hero Hamlet queries on two fronts about how life turns rotten.

Answers next week

Points to Ponder

1 A fly at the end of a metre rule hops to the half-way point, then back to the quarter-way point, and so on back and forth with each hop half the length of the preceding one. Where does she end up? If each hop takes one second, how long will it take?

2 Can a circle always be drawn through three points?

3 Each of the snooker balls has an integer on it in such a way that the three corners of every triangle findable in the array have an odd sum. What is the maximum number of even numbers there can be in the array? And which numbers should they be?

4 What space greeting would be appropriate for Tuesday next?

comments to: indy@puzzlemaster.co.uk