Enrolment Puzzle

[Joseph Bolas]

Here is another puzzle from the PerplexCity series:

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?

[Kirk Bevins]

A good maths puzzle this - I've used it before, apart from the extension question - so I'll keep quiet.

[Howard Somerset]

Very nice puzzle. I can certainly see the mathematical principle which is being used here, but never seen it wrapped up in such a way. I think I've processed the wrapping correctly, and am now PMing my solution to Joseph.

btw, I'm up early this morning, rather than going to bed late. Got to be in Manchester before 6am. Took this puzzle to bed with me last night for some nice bed-time reading. Early morning baby-sitting is not a thing to be recommended.

P.S. Just noticed your siggy, Joseph. So that's a couple more printed out, and will be taken with me to Manchester.

[Joseph Bolas]

Very nice puzzle. I can certainly see the mathematical principle which is being used here, but never seen it wrapped up in such a way. I think I've processed the wrapping correctly, and am now PMing my solution to Joseph.

Thank you . I have recieved your PM Howard and it its correct

P.S. Just noticed your siggy, Joseph. So that's a couple more printed out, and will be taken with me to Manchester.

I decided to use my sig to advertise my puzzles

[Kai Laddiman]

Can someone just throw away or ban those darn PerplexCity cards?

[Joseph Bolas]

Can someone just throw away or ban those darn PerplexCity cards?

I personally think these are brilliant puzzles and are fun to solve.

Originally in the first series, there was a Receda Cube, you had to find on Earth and the first person to find it got the prize of £100,000.

[Jason Larsen]

That sounds like one heck of a school!

[Joseph Bolas]

Its been a week since this puzzle was posted so time to reveal the answer.

As the puzzle states that the ritual was started 20 years ago, this present year must be the 21st and the number of students required is 441 (21 x 21).

Well done to all who solved it