10. Person A writes down the number 1. For any number $n$ already written, A then writes down $5n$ and $5n+1$, provided they are both less than 1000. Person B calculates the sum of any two different numbers that A has written. How many different sums can B obtain?
(Bulgaria)
10. Represent the sum of A's number and B's calculation in base 5.

A's maximum number is $(11111)_{5}$, and his number only includes the digits 0 and 1.

B's calculated number only includes the digits $0, 1, 2$. Since B adds two different numbers, the sum must have at least one digit 1, and it cannot have only one digit 1 without a digit 2. B's maximum number is $(22221)_{5}$.

Among the five digits, there are three choices each, but first, we need to exclude numbers that do not contain the digit 1, and then exclude numbers that contain only one digit 1 without a digit 2.

Thus, B obtains $3^{5}-2^{5}-5=206$ different sums.