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By a freak of nature and an error by the author, it's nearly the start of a new school year in 2016 and Mr Stubbins (the caretaker at Farthingbottom School) is getting nervous. Since he started working at the school in 2001 he has been plagued by repeated acts of vandalism or, to be more precise, one specific act of vandalism - the theft of one of his 'H's. The entrance to the school is marked with 20 stone uppercase letters, each around 2 feet high and pranksters keep removing one. Sometimes he finds it hidden in the bushes some way away from the entrance, sometimes it disappears without a trace and he has to order a new one. It only happens (at most) once per year and he has come to conclude that it is some sort of rite of passage for the new intake of pupils at one of the 3 nearby boarding schools. These are the dates of the mornings each year when this calamity has been discovered:

2015: 13 September
2014: 24 September
2013: 06 September
2012: 16 September
2011: 28 September
2010: 08 September
2009: he camped out all night every night in September and nothing happened
2008: one morning near the end of the month
2007: can't remember, but it was a Wednesday morning
2006: nothing happened
2005: a Sunday morning
2004: one morning near the middle of the month
2003: one morning near the end of the month
2002: nothing happened
2001: around the middle of the month

The three suspected schools are Allbrightnow Academy, Bodgingworthy Boys and Consternation College. Each of these runs a couple of late-evening clubs for their pupils which none of them would dream of missing out on. The pranksters wouldn't have been able to carry out their mission on an evening when they had a club to attend.

  • Allbrightnow Academy has Origami on Monday and Astronomy on Friday
  • Bodgingworthy Boys has Electronics on Wednesday and Film Club on Sunday
  • Consternation College has Survival Skills on Sunday and Weightlifting on Friday.

Should Mr Stubbins be prepared for intruders this year? If so, which night are they likely to come and which school are they going to come from?

Note: Assume the schools are in the UK.

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  • $\begingroup$ Does the UK have holidays in September, like the US does on Labor Day? $\endgroup$ – Kingrames Aug 26 '15 at 15:25
  • $\begingroup$ I am guessing this is for 2016? $\endgroup$ – dramzy Aug 26 '15 at 15:26
  • $\begingroup$ @Kingrames There are no UK national holidays in September $\endgroup$ – Gordon K Aug 26 '15 at 15:31
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    $\begingroup$ "2001: around the middle of the month" Really, boys? Bit of a rough time to go around vandalizing. Sheesh! Have some consideration! That was right after 9/11! $\endgroup$ – Kingrames Aug 26 '15 at 15:50
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    $\begingroup$ You know I just realized, if he were smarter, he'd take the opportunity to move the other h, and he'd end up with a sign that said "Farthingbottom's cool." $\endgroup$ – Kingrames Aug 26 '15 at 18:38
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Allbrightnow Academy are the culprits and they will attack on the evening of September 1st.

Explanation:

Each of the dates is on the new moon of that month. If the new moon occurs before midday BST, it is the evening of the day before and therefore discovered that morning, otherwise it is at the end of the day and discovered the next. The two years where nothing happened were fridays, that rules out Bodgingworthy Boys. In 2008, the new moon was 09:12 on the 29th which was a Monday, therefore it would have been done on the Sunday which means Consternation College couldn't have done it

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  • $\begingroup$ Turns out I was using UTC time, not BST.. didn't help $\endgroup$ – George Aug 27 '15 at 7:40

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