Joined: 18 Oct 2004 Posts: 1842 Location: London
[S2] [Dice Set] #167 Enrolment 610 points Puzzle Designer: Sente
20 years ago the academy began a now annual ritual where a number of the students line up in front of their lockers. The master of the academy blows a whistle and every student opens their locker. The whistle is blown again and every 2nd locker is closed. On the third whistle, every 3rd locker is changed from open to closed or vice versa. This pattern continues until the whistle has been blown the same number of times as there are students.
In each successive year the aim is for the minimum number of students to assemble as to increase the number of lockers left open at the end by one. Given that only 1 locker was left open in the inaugural year,
how many students are needed this year?
Fri Mar 09, 2007 11:37 am
Joined: 07 Apr 2005 Posts: 352
Two hours have passed since my last entry, yet I would scarcely believe it has been more than two minutes if not for my chronometer. The cause of this time dilation was - and is - a pirate vessel.
I initially put this down to a high-spirited jape by a crewman but upon being handed a telescope by Green, I had to admit that the ship on the horizon did have a very piratical appearance about it viz cannons, black and white flag, ghastly figurehead. Green seemed rather excited about the whole thing.
"Avast Kennard, step up smartly! A swab on yonder crow's nest sighted those blaggards aft - what say we take those scurvy tars broadside, and show them no quarter!" he said with a flourish.
"Green, this is no time for nonsennse. I'm going to find Captain Harrison," I replied.
"Belay that talk! Cap'n Harrison... er... does not want to be disturbed," said Green, evidently having exhausted his entire repertoire of pirate talk. I looked up towards the quarter-deck to see the Captain conferring with his officers in a state of forced calm. The PRS Exsuscito is no vessel of war, and with horologists being ill-suited to martial pursuits, fighting was not an option. We either had to run or surrender.
Sure enough, we accelerated, and for the past two hours, the pirates have not gained on us - but neither have we widened the distance. One of the horologists, Fischer, has been arguing with Harrison for some time. I fear it may be related to the black and white flag I saw in his cabin yesterday...
Fri Mar 09, 2007 12:07 pm
Joined: 06 Dec 2005 Posts: 37
The way i worked it out gave the following:-
Spoiler (Rollover to View):
if year 1 there was 1 student then no. of open lockers =1
in year 2 we need 4 studentsto have no.o f open lockers=2
in year 3 we need 9 students to have no. of open lockers = 3
so in year 20 (i.e. last year) then no. of open lockers required = 20 therefore no. of students required = 400.
So in conclusion to have 21 open lockers we need 441 students.
Mon Mar 12, 2007 9:46 am
I got the same but when I went to enter it on the site it said incorrect, is there any thing im missing
Mon Mar 12, 2007 11:55 am
I can confirm that
Spoiler (Rollover to View):
441 is correct.
Mon Mar 12, 2007 6:25 pm
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