A passenger left their belongings in an automated storage locker, and when they came to retrieve their items, they realized they had forgotten the number. They only remember that the numbers 23 and 37 were in the code. To open the locker, the correct five-digit number must be entered. What is the minimum number of codes that need to be tried to definitely open the locker?

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Let's consider several cases.

1) The number contains the combination 237. It can be placed in the number in three ways: **237, *237*, 237**. In each of these, each of the remaining digits can be chosen in 10 ways. In total, we get $3 \cdot 10^{2}=300$ numbers. 2) The number contains the combinations 23 and 37, with 23 located to the left. The remaining digit can be chosen in 10 ways and inserted into one of three positions. In total, 30 numbers.
2) The number contains the combinations 23 and 37, with 23 located to the right. Another 30 numbers.

It remains to note that the numbers 23723, 23237, 23737, and 37237 have been counted twice.

## Answer

356 numbers.