Solution: We can use the following Binary number system to solve this puzzle. First, number the bottles from 1 - 1000. Convert the bottle number to binary. Number the rats D1, D1, D2, ...., D9 representing the binary digits. Then, rats will drink wine in the following rule: Binary number of bottle 1 is 0000000001. Rat D1 will drink wine from bottle 1 Binary number of bottle 5 is 0000000101. Rats D1 and D3 will drink wine from bottle 6. Binary number of bottle 12 is 0000001100. Rats D3 and D4 will drink wine from bottle 12. ..... Hence, by seeing which rats have died, we can figure out which bottle is poisoned. For example: If rats D3 and D4 die, then we know the bottle 12 is poisoned. 1000 bottles can be represented with 10 binary digits (binary number of bottle 1000 is 1111101000) , and we have 10 rats (each rat represents 1 digit), so we are able to use 10 rats to test 1000 bottles of wine.
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