After keying in the combination, rotate the handle clockwise by pi/2 then counterclockwise by pi.

After keying in the combination, rotate the handle clockwise by pi/2 then counterclockwise by pi.

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4 - by substitution

5 - by calculation (any faster way ?)

3 - evidently as only the cube will remain

1 - thanks to wikipedia

Nice to do some simple mathematics once in a while :D

And to learn about yet another of Euler's achievements

Oh! I read it as x^(3/2) and was a little confused as to how the third derivative was in {1,2,3,4,5}.

Me too, then I remembered "Please Excuse My Dear Aunt Sally"... Exponent before Division.

I think the notation is ambiguous: the question isn't which operation to do first, but whether it is the x^3 is divided by 2, or just the 3. Still, might as well go with the only one that makes sense.

The first one can also be factored

x³ - 4x² + 6x - 24 =

x²(x-4) + 6(x-4) =

(x²+6)(x-4)

The only real root is 4

An even quicker way.

Notice x^3+6x=4x^2+24

so, x(x^2+6)=4(x^2+6)

thus x=4

how can you substitute the first one?

@brainyac you forgot to turn the know a quarter turn clockwise and half a turn anticlockwise after entering the combination

A (slightly) faster way for digit 2:

This matrix is obviously singular (since the second row is twice the first one), so it has one eigenvalue 0. The other eigenvalue therefore is equal to the trace, which is 5.

Nice to point this out... I hadn't observed this and had done for direct computation! Thanks

This is definitely the approach I would take! I work with matrices wayyy too much so eigenvalues are second nature.

We could also hope they have publicly available WiFi and use Wolfram|Alpha :-)

This isn't actually correct since the derivative of a function is a function again, not a number (the function may be constant, but it is not

aconstant).Actually, it's an expression, not a function (there is no equals sign or other mapping to an output). Coincidentally, the label next to the third button on the door is also an expression that happens to be constant.

yeah, but there's nothing wrong with canonically identifying the constants with their imbedding in the ring of functions.

You never met Mr H. B. Curry, did you? ;)

So what about digit five?

Judging by this discussion, the Math clubbers are still arguing about it.

There is no fifth digit in the combination. The numbers on the door are buttons.

Isn't the third derivative of the given function = 6? Since (x^3)' = 3x^2, (3x^2)' = 6x, and (6x)' = 6? So you can't actually get in...

it's x^3/2 ... so (x^3/2)' = 3x^2/2 and (3x^2/2)' = 3x ans (3x)' = 3.

So what happens when an Eng Phys students enters the door and says that Heaviside was one of the greatest mathematicians because he made Laplace Transforms easy to deal with in the engineering world?

I'm just poking fun

He gets hit with a fast Fouier transform.

I prefer to think of it as a rotation by -pi/2 followed by one of pi.

why do I feel the button 2 is too neglected?? :P

Okay, crazy real-life story about an easier version of this.

So, at SFU circa 2000, the Math Society common room had a door locked with a lock like this. The lock's combination was the unique solution to a*b+c=d*e, where (a,b,c,d,e) is a permutation of (1,2,3,4,5). (note on use: press a&b at the same time, then c, then d&e). It also contained a filing cabinet with a bunch of old exams, useful for studying.

So, in a third-year elective math course (presumably populated entirely by math majors plus me), the TA (Tim) mentioned all this as a suggestion on where to get study advice for the midterm. And so he finishes explaining, and after a pause, one student says "what's the answer?" Poor Tim, he's just an angel of a guy, so kind-hearted. In his shoes I'd have said "if you can't exhaustively check 5! cases, you deserve to fail", but he was just speechless.

1*3+5=2*4

However, 1 and 3 are interchangable, as are 2 and 4.

It doesn't matter that they're interchangeable, since they're pressed at the same time.

Why use the words clockwise and counter-clockwise? First rotate the handle by pi/2, then by -pi ;)