## Task B-2.4.

Andro and Leo are guessing a four-digit number that the other has thought of. In doing so, they must uncover some information about their number. Andro's number has all different digits, and the first and last digits are odd numbers. Leo's number does not have to have all different digits, but all of its digits are of the same parity and different from 0. Based on the revealed information, who has a higher chance of guessing the number that the other has thought of?
## Solution.

Andro's number can be written as $\overline{a b c d}$. The digit $a$ can be chosen in 5 ways (since it must be an odd number), and the digit $d$ can be chosen in 4 ways because it must be of the same parity but different from $a$.

For the digit $b$, there are 8 possible choices left (all digits except the two chosen), and for the digit $c$, there are 7 possible choices.

Therefore, Leo needs to guess one of $5 \cdot 8 \cdot 7 \cdot 4=1120$ possible numbers.

Leo's number has all four digits of the same parity and can repeat. Among the 10 digits, there are 5 odd digits and four even digits (excluding zero).

Therefore, Andro needs to guess one of $5^{4}+4^{4}=881$ numbers.

Since Andro chooses from fewer numbers, he has a higher chance of guessing the opponent's number.