1) How many pairs of rabbits will be produced in a year, beginning with a single pair, if in each month each pair bears a new pair, which becomes productive from the second month on?
2) What is the next number? 0,1,1,2,1,3,1,3,2,3,1,5,1,3,3,4,1,5,1,5,…
3) What is the next number? 5,17,37,5,101,5,197,257,5,…
4) On each row place a letter which can be substituted for the second letter of the words either side so that two other words are formed. When completed a word will be read downwards. What is it?
ALTER ACHES
POINT FIRES
BENCH SPITE
SHAKE SHORE
LIBEL MINOR
Answers to the November puzzles:
1) About 83%, ie 0.83190737…, the reciprocal of Apery’s number.
2) This belongs to Ramsey theory. The upper bound is called Graham’s number and is so large it can’t be written like an ordinary number. It is vastly beyond Skewes’s number, which is 10 to the 10 to the 10 to the 34. The number of atoms in the universe is much smaller, being about 10 to the 75. Karl Sabbagh says that most experts in Ramsey theory believe the correct answer is 6. (from Sabbagh’s The Riemann Hypothesis, p 145)]
3) Reaction
4) A [the sequence consists of the first and next-to-last letters of the months]
