Happy Birthday!

Let the probability two of them share a B'day be P(A).
$P(A) = 1 - P'(A) = 1 - \displaystyle \prod_{n=0}^{22}\left(\dfrac{365-n}{365}\right) = 1 - 0.492702765 \approx 0.5073$

$x = \left \lfloor 100 \times 0.5073 \right \rfloor = 50$

We calculate $P'(A)$ as the probability that no pairs share the same birthday.

There are $\frac{23 \times 22}{2}=253$ pairs. The probability that 2 people have different birthday is $\frac{364}{365}$ . The probability that no pairs among $253$ pairs share the same birthday is $P'(A)=(\frac{364}{365})^{253}\approx 49.27\%$ . So, the probability that there exists 2 people share the same birthday is $P(A)=1-P'(A)\approx 50.72\%$ . The answer is $\boxed{50}$ .

This is perhaps known as the birthday paradox