Enigma 1287: Blue Bin
11 October 2014
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From New Scientist #2445, 1st May 2004 [link]
George’s blue wheelie bin (used for recyclable paper) was emptied by the council on 1 April 2004. It is emptied every fourth Thursday, and we presume that this schedule will continue indefinitely, in spite of official holidays. The next collection will be on 29 April giving, unusually, two collections in one calendar month. Looking to the future, when are the first years in which the following events will occur?
(1) One calendar month in the year has no collection day.
(2) There are two collections in one calendar month in the year.
(3) No month in the year has two collection days.
(4) Two months in the year each have two collection days.
(5) February has two collection days.
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.