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#158 League of nations

The TV sporting highlight of my childhood was always the Five Nations rugby championship, which involved a series of matches between England, Scotland, Wales, Ireland and France.

Every fortnight, on Saturday afternoon, there would be two matches, with the fifth country having the day off.

The fixture list had an elegant symmetry to it. Each country played every other country once, with two matches at home and two away, and each country alternated between playing at home and away.

I recall that in one year, the fixtures on the opening Saturday were Ireland vs England and France vs Wales, and that, on the third Saturday on which matches were played, Wales competed at home.

If those memories are correct, what were the final two matches of the competition?

Solution next week

#157 Weather or not

Solution

Eileen has a better chance of winning than Ike. Call a rainy day R and a no-rain day N. Eileen chooses NRR and Ike RRN. In the first three days, they each have an equal (1/8th) chance of being right.

But if the sequence RRN first crops up after day three, then NRR must have occurred a day earlier unless it rained on every previous day.

So for Ike to win, the sequence has to be RRN or RRRN or RRRRN鈥� etc, for which the probability is 1/8 + 1/16 + 1/32鈥�, which adds to 录.

The chance of Eileen winning is therefore 录, three times as likely as Ike. This is a variation on the classic game of Penney Ante (or Penney鈥檚 Game).

Quick quiz #142

1 What is the fragmented rock, dust and other material ejected in volcanic eruptions called?

2 Which Soviet biochemist was a leading proponent of the 鈥減rimordial soup鈥� theory of the origin of life?

3 What name is given to the region of space that our galaxy and others are being pulled towards?

4 In what year did Marie and Pierre Curie discover radium and polonium?

5 The hardened wing casings of beetles are more formally known as what?