4. Misha, over the course of a week, picked an apple each day and weighed it. Each apple weighed a different amount, but the weight of each apple was a whole number of grams and ranged from 221 grams to 230 grams (inclusive). Misha also calculated the average weight of all the apples he picked, and it was always a whole number. The apple picked on the seventh day weighed 225 grams. How much did the apple picked on the sixth day weigh?
Answer: 230 grams.

Solution: Each apple weighed 220 grams plus an integer from 1 to 10. From the numbers 1 to 10, we need to choose 7 numbers such that their sum is divisible by 7. One of these numbers is 5, so we need to choose 6 from the numbers $1,2,3,4,6,7,8,9,10$. The smallest sum of six of these numbers is 23, and the largest is 44. Adding 5, we get numbers from 28 to 49. In this range, there are 4 numbers divisible by 7: 28, 35, 42, 49. Meanwhile, the sum of the weights for the first 6 days must be divisible by 6. From the numbers 23, 30, 37, 44, only the number 30 satisfies this condition. Thus, the total weight for the first 6 days was $220 \cdot 6 + 30$ (we will simply write 30, and add the multiple of 220 at the end). The sum of the weights for the first 5 days must be divisible by 5. The possible range for 5 days is from 16 to 40, and the numbers that fit are $20, 25, 30, 40$. However, the total weight for 5 days is less than that for 6 days, so it must be less than 30, i.e., 20 or 25. However, the difference between 30 and 25 is 5, and the number 5 is already used. Therefore, the weight of the apples for 5 days is $220 \cdot 5 + 20$, meaning the apple picked on the 6th day weighed $220 \cdot 6 + 30 - (220 \cdot 5 + 20) = 230$ grams. This value is valid, as the apples picked over the week could have weighed 221, 223, 222, 226, 228, 210, 205 grams.