4. How many numbers divisible by 4 and less than 1000 do not contain any of the digits $6,7,8,9$ or 0.
Answer: 31. Solution. According to the condition, these numbers consist only of the digits 1, 2, 3, 4, and 5. Out of such numbers, only one single-digit number is divisible by 4: 4. Among the two-digit numbers, the following are divisible by 4: $12, 24, 32, 44, 52$. If we prepend 1, 2, 3, 4, or 5 to all these two-digit numbers, they will also be divisible by 4. There will be no other three-digit numbers divisible by 4 (the rule for divisibility by 4). Therefore, the total number of such numbers is: $1 + 5 \cdot 6 = 31$.