Nope, I honestly have no idea, but I expect the number of combinations to be around a billion.
I think you could start with the amount of possible perfect tenths on the piano's 88 keys. There are 52 white keys, so that's 42 possible perfect tenths. The number of diminished tenths (an interval of 9,5 notes, e.g. F to G#(with an octave in between)) 60. But you could play a perfect and a diminished tenth at the same time (if you had flexible fingers), as long as they fall into each other.

Yang-Mills and Mass Gap, solve

Huh?

Come again? When I search for "Yang-Mills" I get this: http://en.wikipedia.org/wiki/Yang-Mills which does not seem overly related (maybe I'm stupid, but what does quantum chromodynamics have to do with either music or counting problems...!?). For "Mass gap" I get http://en.wikipedia.org/wiki/Mass_gap and have the same question.

On a (presumably related??) note, I might as well yell: "SAT problem; let a solver construct the BDD and count the number of possibilities", but I'm old-fashioned and figure puzzles should be solved with understanding, not throwing overpowered tools at them and getting an answer which is correct, but which you don't understand.

The laws of quantum physics stand to the world of elementary particles in the way that Newton's laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics.

if you solve that you are one of the smartest humans in history

You should also post your solution here before taking any other action.

Since I didn't get to post a problem before and in order to get us back on track here's a fairly straightforward one:

A man owns 7 different coloured pairs of gloves, 7 different coloured pairs of socks to match his gloves, and 7 different coloured ties to match these. He keeps them all in the same drawer without the gloves and socks paired up. One morning he wakes up hungover and late for an important meeting, in his confused and panicked state he is unable to distinguish between the three types of garment and starts grabbing randomly. How many items must he grab before he is assured of a matching set of gloves socks and tie?

assuming he`s unlucky and picks in order, he can pick 7 pairs of socks and 7 pairs of gloves without having 3 pairs of everything, the next pick which then is a tie will give him a complete set. So he`ll have to pick 7x2+7x2+1 =29 iteams before he`s guaranteed a set.

so the answer is 29.
(Note if a pair of socks/gloves= 1 item the answer is 7+7+1=15.

Splendid work, you are correct.

Okey, my turn to post a problem :D

I`m a 60kg astronaut,who have gone outside my spaceship to fix the cable which is used to secure people on the outside of the spaceship. Unfortunately do I lose control and start slipping away from the spaceship, when I`m 50m away I realize I`ve to do something, but the only thing I\ve is my 5kg toolbox :(

What must I do to get back to the spaceship, and will my 20min left of Air be enough to survive back to the spaceship?

Tell your buddy to come and get you? Throw your toolbox as hard as you can in the opposite direction to the door? Reflect on how you deserve to die for your appalling reflexes?

throw your toolbox in the opposite direction. newtons third law, for every action there is an equal and opposite reaction. and there will be no external forces, so you should remain in motion, and that idea would follow his first law.

Burgoo,
That leaves two questions:
- At what speed should you throw away your toolbox?
- Will the twenty minutes of oxygen remaining suffice?

Assuming the spaceship isn't moving, assuming that just because youre in space gravity is not acting on you, assuming the speed you're moving away from the spaceship is what? 0?

Yeah, yore right about the concept, Burgoo, but as RvW pointed out, you didn`t solve the whole problem..

I also see that the last part wasn't really good explained, it`s supposed to be:
Whit How much Force do you have to throw the toolbox, to get back in 20 min.

Also, to clear any confusion:
-the spaceship is not moving
-"I"`m not moving
-Universal gravitation is neglected
(always assume that^^ unless otherwise is told)

Sorry for the double post.

gah i dont remeber those equations thats like elementary physics, gg

Okay, new problem since my old one was probably too complicated.

Prove that x!-1 is not always a prime number.

x e {0,1,2} ?

If you restrict x>2, then
x=5

5!-1=120-1=119=7*17