1000 Apple distribution problems

Old Wang has 1000 apples in boxes numbered 1-10. No matter how many apples a customer needs to buy, he can always follow the appropriate boxes numbered, the total number of apples in these boxes is exactly the same as the customer's needs. How did Old Wang do that?

Tip: this interesting question is about binary sensitivity.

 

Answer: We can use the binary method to allocate the number of apples in each box.

Box No.: 1 2 3 4 5 6 7 8 9 10

Apple count: 1 2 4 8 16 32 64 128 256 489 (512-23)

Why is the last box 489? Because the total number of apples is 1000. If the last box is 512, the total number will exceed 1000, and the total number will be 489, only in this way can the customer be freely combined as long as the customer needs to satisfy the customer