What music you play when tackling a difficult programming problem?

None. Music by it's very nature is designed to draw you into it's world. If you want background nose, use background noise.

I'm listening mostly to ambient and instrumental music. MusicForPrograming has a great selection of them: http ://musicforprogramming.net

Electro-house or hard trance. Something with a solid repetitive beat and minimal to no lyrics (occasionally those lyrics may be in a foreign language).

Nick Cave's just released "Ghosteen" is perfect. Quiet, beautiful soundscapes.

Nightcore white noise wardrums whatever is playing as long as it's not my native language