And it looks like the birthday puzzle has been thoroughly analyzed. I came up with the same formula that the paper presented by RA had. My calculator blows up at about 69!, and I didn't want to figure things out usings logs, so I cheated and used Excel.
2 364 365 0.997260274 3 363 365 0.994520548 4 362 365 0.991780822 5 361 365 0.989041096 6 360 365 0.98630137 7 359 365 0.983561644 8 358 365 0.980821918 9 357 365 0.978082192 10 356 365 0.975342466 11 355 365 0.97260274 12 354 365 0.969863014 13 353 365 0.967123288 14 352 365 0.964383562 15 351 365 0.961643836 16 350 365 0.95890411 17 349 365 0.956164384 18 348 365 0.953424658 19 347 365 0.950684932 20 346 365 0.947945205 21 345 365 0.945205479 22 344 365 0.942465753 23 343 365 0.939726027 24 342 365 0.936986301 25 341 365 0.934246575 26 340 365 0.931506849 27 339 365 0.928767123 28 338 365 0.926027397 29 337 365 0.923287671 30 336 365 0.920547945 0.293683757 0.706316243
P.S. No stinking leap years.
I don't do much math at the moment, but I always thought it was unfortunate that calculators didn't have a birthday problem button. I suppose it's easy enough to program though.
I previously thought it was a stunning coincidence that my two brothers' birthdays were the same as my best friend and her husband's.