B1. The banker wanted to open one of the vaults but had forgotten the code. He knew that the first two characters of the code were the letters B and Ž, but he didn't know which came first. He also knew that the code continued with a four-digit number, in which each of the digits 2, 5, 7, and 9 appeared.

A How many possibilities are there for forming this code?

B What percentage of the possibilities does the banker have to guess the correct code on the first try?

C Later, the banker remembered that

- the code starts with the last letter of the alphabet,
- the four-digit number in the code is divisible by 5,
- the hundreds digit of this number is less than the thousands digit,
- the tens digit is equal to the sum of the digits in the hundreds and thousands places.

Write down the code.
B1. The number of possible combinations is $2 \cdot 4 \cdot 3 \cdot 2 \cdot 1=48$. We can also write them down and count them.

B The banker has $\frac{1}{48} \approx 0.02=2 \%$ chance of finding the correct code on the first attempt.

C The code starts with the letter Ž, followed by the letter B. The four-digit number that follows the letters ends with 5. The digits 2, 7, and 9, which remain available, are arranged according to the following key: 9 in the tens place is the sum of the digits 2 and 7 in the hundreds and thousands places. Considering that the hundreds digit is less than the thousands digit, we get the code ŽB7295.

Scoring: Total: 7 points
A For combinations with letters: 2 possibilities ..... $1 \text{p}$
For combinations with numbers: 24 possibilities ..... $1 \mathbf{p}$
The total number of combinations is 48. ..... $1 \mathbf{p}$
B Calculation: $\frac{1}{48}=0.02=2 \%$ ..... $1 \mathbf{p}$
Answer: The banker has a $2 \%$ chance of finding the correct code on the first attempt. ..... $1 \mathbf{p}$
C The code is ŽB7295. ..... $2 \text{p}$