1. What are the chances that three positive whole numbers, chosen at random, have no proper factor in common?
2. Take any number of people, list every possible committee that can be formed from them, and consider every possible pair of committees. How many people must be in the original group so that, no matter how people are assigned to committees, there will be four committees in which all the pairs fall in the same group, and all the people belong to an even number of committees?
3. In each row, place two letters at the beginning of the word to form a longer word.
FILL
QUIT
RED
SET
When completed, the eight letters used will give a word reading downwards. What is it? (with thanks to British Mensa)
4. What is the next letter in this sequence? JRFRMCAIM?
Answers to the October puzzles:
1) The first number is Roman numeral XXIII. Take the last line and place it on top of the II at the right of the equation. The II becomes "pi", and at the left we have XXII/VII.
2) From Alice in Wonderland, A Caucus-Race and a Long Tale:
…Stigand, the patriotic archbishop of Canterbury, found it advisable – ‘"
"Found what?" said the Duck.
"Found it," the Mouse replied rather crossly: "of course you know what ‘it’ means."
"I know what ‘it’ means well enough, when I find a thing," said the Duck, "it’s generally a frog or a worm. The question is, what did the archbishop find?"
3) The n in the numerator and denominator cancel out, leaving "(1) si x = ?" The result is: six = 6.
4) Dentil, Pistil, and Instil.
Answer to N&Q4 Puzzle, this issue: Victoria’s Restaurant.
