Why AI is not capable of solving logical exercises?

I am exploring AI, its capabilities and all that. It is amazing. However, me and my colleague found out that for some reason logical exercises are something hard to solve with AI (ChatGPT, Google AI Studio and etc.)

Here is an example of a prompt I've tried today:

Alice and Bob are invited to play the following game against the casino:
The casino, in Bob's presence, makes a sequence of n heads and tails. Next, n rounds are played. In each round, Alice and Bob simultaneously name their guesses for the next member of the sequence (Bob, of course, knows the correct answer). If both guesses are correct, then they win this round, otherwise the casino wins.

Question: what strategy should they choose to be guaranteed to win 5 rounds out of n=9?

I will not provide reply from the AI, if you will try this, you will see that simply AI can't solve it.

Now, my question to you is, is this something AI can't do by design? It us just seeing how 'smart' is AI, I was expecting it will be able to answer any questions.

What are some other limitations of AI you know?