Two of the Quiz Master Shop neighbours went on holiday at the same time, and both went for ten days. However, they went to different resorts and, as they were holidaying in the UK they took out rain insurance.
The insurance policies worked as follows: for each rain-free day they paid £1; however, for an isolated day of rain they received £1, for two consecutive days of rain they received £3 (ie one plus two), for three consecutive days of rain they received £6 (ie one plus two plus three), and so on up to a maximum of £55 if it rained for ten solid days!
When they returned from their holidays they compared notes. Neither had had very good weather, and between them they were in profit to the tune of £40, although they had received different amounts. And they discovered that the weather in both resorts had been identical for the first six days.
What happened in the two resorts on the seventh day?
There are a number of combinations that will gain £40 for the two holidaymakers (the numbers in brackets are the wet days):
£36 (8 +1) and £4 (several)
£34 (8) and £6 (several)
£30 (7 + 2) and £10 (several)
£27 (7 + 1) and £13 (4 + 3)
£26 (6 + 3) and £14 (5 + 1 + 1)
£25 (7) and £15 (5 + 2 or 4 + 3 + 1)
£22 (6 + 2) and £18 (4 + 4)
£21 (6 + 1 + 1) and £19 (6 + 1 or 5 + 3)
In only the last case could there be six consecutive days at the two resorts that were the same. That is the first six days in both resorts were rainy and the seventh day was dry in both, ending the run of bad weather.