999?

You're both wrong according to Wikipedia (although that bit about lines connecting and accidentally calling 111 is true... but then 999 is a very commonly butt-dialed number, leading to an enormous number of fake calls (112 and 911 don't have that problem)).

Apparently it was all down to practical money saving reasons. It was easier to modify the pay phones of the time to dial 999 for free than any other series of numbers (because 0 was already free). Bah, humbug. What a ridiculous reason. I much prefer the reasons presented by the people here on this page. Anyway, here's Wikipedia's more detailed explanation: http://en.wikipedia.org/wiki/999_%28emergency_telephone_number%29#History