Birthdays problem

I have a book I got as a kid, the book is called "Challenge", and it contains a bunch of questions (and answers), including the birthday pair question.

If you have 28 guests at a party, the odds are almost 2 to 1 that two of the guest will have the same birthday (65.446% chance).

That particular article also listed the 'magic number' for various numbers of party guests, for example:

Magic # for party of 6 is 23, meaning that 23 is the limit of the # of choices you can offer and still expect a duplication. For a party of 6, you can use, for example:
1) Month of birth
2) Choice of card in any one suit
3) Choice of positions on a football team


Magic # for party of 8 is 42
1) Date of month they were born
2) Choice of letters in the alphabet


Magic # for party of 12 is 99
1) Choice of any card in the deck
2) Exact amount of change in pocket or purse
3) Choice of any state in the U.S.


Other magic #s:

5=16
7=32
9=54
10-68
11=82
15=156
18=226
20=280
25=441
30=637

One time, when I worked in an office with 16 people, we found that there were not one, but two pairs of individuals who had the same birthday...I was one of the birthday twins...that's certainly more than one would expect with only 16 people, but it's also more common than one would think...

I'd guess that "Challenge" is no longer in print, but it was copyrighted in 1968 by Hallmark Cards, Inc, Lib of Congress Card # 68-16436.

The theory is all shown here.

http://www.cut-the-knot.org/do_you_know/coincidence.shtml