For the sequence of numbers starting

$$
1,3,4,7,11,18, \ldots
$$

it holds that each number starting from the third is the sum of the two preceding ones.

What is the last digit of the 2023rd number in this sequence?

Hint. Use the sequence formed by the last digits to help yourself.
The last digit of each number corresponds to the remainder of that number when divided by ten. Therefore, it is sufficient to deal with the sequence of corresponding remainders:

$$
1,3,4,7,1,8, \ldots
$$

which means the sequence where each number starting from the third is the remainder of the sum of the previous two when divided by ten. This sequence repeats every 12 terms:

$$
1,3,4,7,1,8,9,7,6,3,9,2 ; 1,3, \ldots
$$

Thus, for example, the 1st, 13th, 25th, 145th, or 2017th term of the sequence consists of the same numbers.

The number 2023, when divided by 12, gives 168 with a remainder of 7. Therefore, the 2023rd term of this sequence is the same as the 7th term, which is the number 9.

The 2023rd number in the given sequence ends with the digit 9.