Read the original question here
Answer: The years were (a) 2000 (b) 2005
The winner is Jae Eon Lee of Surbiton, Surrey, UK. There were 97 entries.
Worked answer
February must contain at least 3 complete calendar weeks, during which I do 9 runs.
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In a normal year (28 days) the other 7 days can be spread before and after the 3 weeks 7-0, 6-1, 5-2 or 4-3.
- If 7-0, I must add 3 more runs.
- If 6-1/5-2, I could add 3+1 or 3+0 or 2+1 or 2+0 more runs.
- If 4-3, I could add 2+2 or 2+1 or 1+2 or 1+1 more runs.
In a leap year (29 days) the other 8 days can be spread before and after the 3 weeks 8-0, 7-1, 6-2, 5-3 or 4-4:
- If 8-0/7-1, I could add 4 or 3 more runs.
- If 6-2, I could add 3+1 or 3+0 or 2+1 or 2+0 more runs.
- If 5-3, I could add 3+2 or 3+1 or 2+2 or 2+1 more runs.
- If 4-4, I could add 2+2 or 2+1 or 1+2 or 1+1 more runs.
So the maximum number of runs is 14, achievable only in a leap year in which February 1st is a Tuesday (5 days before the 3 weeks, 3 days after) or a Thursday (3 days before the 3 weeks, 5 days after).
The last such year was 2000 (before that 1996). The minimum number of runs is 11, achievable if the other days are spread 6-1, 5-2, 4-3, 6-2 or 4-4.
March has 10 days to spread before and after its 3 weeks:
- If 10-0, I could add 5 or 4 more runs.
- If 9-1/8-2, I could add 4+1 or 4+0 or 3+1 or 3+0 more runs.
- If 7-3, I could add 3+2 or 3+1 more runs.
- If 6-4, I could add 3+2 or 3+1 or 2+2 or 2+1 more runs.
- If 5-5, I could add 3+3 or 3+2 or 2+2 more runs.
So the minimum number of runs in March is 12, which must be linked to February’s maximum of 14.
In 2000, March’s days to spread were 4 (March 1-4) and 6 (March 26-31).
So I ran on Feb 1, Feb 3, Feb 5, then 3 weeks, Feb 27, Feb 29, Mar 2/3/4, then 3 weeks, 2 of Mar 26-30 (and Apr 1).
The maximum number of runs in March is 15, achievable only when March 1st is a Tuesday (5 days before and 5 days after the 3 weeks). The last such year was 2005 (before that 1994); this must be linked to February’s minimum of 11.
February’s spread of 5-2 for the other days in 2005 makes this possible: I ran on (Jan 30/31 and) 2 of Feb 1-5, then 3 weeks, Mar 1, Mar 3, Mar 5, then 3 weeks, Mar 27, Mar 29, Mar 31.
