The Lock

[Jezza]

<P ID="edit" class=small>(Edited by Jezza on 11-Mar-07 22:58. To add PS)</P>Al Bear Einstein was sitting quietly one night in his study looking at the instructions for his new digital padlock. It was one of those special locks that you had the digits 1,2,3,4,5,6,7,8,9,0 on it and to open the padlock he was instructed to choose a 4 digit number and if it was correct the lock would open. He was feeling uncomfortable by the instructions because he, as Al Bear always did, found some anomalies in the design.

One of them was that he had found that if he chose the opening code as 3421, it didn't matter which order he typed in the number in it would open, so he could type in 1234 or 2341 and it would open , this was the same for any 4 digit number that was chosen i.e. 6392 could be entered 2369 or 6932.

He also found that he couldn't put the same number in more than once so 9990 or 9900 could were not allowed and every number had to be different.

As he sat in the darkened room sipping his cocoa he thought "This would be an excellent puzzle for the Woody's guys"

Al Bear asks "With the set of rules provided above what is the number of possible combinations this digital padlock can have?"


PS Can I ask for a proof on this one as I have done one and I would like to compare...be it in the form of an Excel spreadsheet or other

[StuartR]

Jezza,

Isn't this <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">how many combinations of 4 can you make from a set of 10 different things? (10*9*8*7)/(4*3*2*1) = 5040/24 = 210</span hide>

StuartR

[Jezza]

Sir, you can have a [choccy bar] <img src=/S/trophy.gif border=0 alt=trophy width=15 height=15>

[StuartR]

<img src=/S/yum.gif border=0 alt=yum width=15 height=15> I haven't had a [choccy bar] for ages. It's just what I need right now.

Good night.

StuartR

[StuartR]

That looks like sound logic to me, and much better laid out than mine. The remains of the half eaten [choccy bar] shall be duly handed over.

StuartR

[Jezza]

Goood Looord, I have never seen the depth of such an answer BRILLIANT and so simple. You can have a [choccy bar] and a mug of steaming [cocoa]

[Tricky]

<img src=/S/bow.gif border=0 alt=bow width=15 height=15> <img src=/S/thankyou.gif border=0 alt=thankyou width=40 height=15>

[Tricky]

<img src=/S/poke.gif border=0 alt=poke width=60 height=17> Jezza -
Excuuuuuse Me.

I know Stuart has already provided you with an answer and I know you've [prematurely] awarded the [choccy bar] but I feel compelled to protest. I do not believe the solution was accompanied with adequate proof. I, on the other hand, have not only solved the puzzle but have added all the proof one should require in the attached spreadsheet.