The correct sample size to get past a probability of 0.5 is 23 people. You should justify this numerically by justifying the following probabilities:

#	P(Match)	
1	0
2	0.0027
3	0.0082
4	0.0164
5	0.0271
6	0.0405
7	0.0562
8	0.0743
9	0.0946
10	0.1169
11	0.1411
12	0.1670
13	0.1944
14	0.2231
15	0.2529
16	0.2836
17	0.3150
18	0.3469
19	0.3791
20	0.4114
21	0.4437
22	0.4757
23	0.5073
24	0.5383
25	0.5687
26	0.5982
27	0.6269
28	0.6545
29	0.6810
30	0.7063