Label the bottles from 1 to 1000, and similar to the locker problem, have each rat drink from bottles using a specific pattern as follows:
Rat 1: Drink from every bottle
Rat 2: Drink from every second bottle (bottles numbered 2, 4, 6 ...)
Rat 3: Drink from every third bottle (bottles numbered 3, 6, 9 ...)
Rat 4: Drink from every fifth bottle (bottles numbered 5, 10, 15 ...)
Rat 5: Drink from every seventh bottle (bottles numbered 7, 14, 21 ...)
Rat 6: Drink from every eleventh bottle (bottles numbered 11, 22, 33 ...)
Rat 7: Drink from every thirteenth bottle (bottles numbered 13, 26, 39 ...)
Rat 8: Drink from every seventeenth bottle (bottles numbered 17, 34, 51 ...)
Rat 9: Drink from every nineteenth bottle (bottles numbered 19, 38, 57 ...)
Rat 10: Drink from every twenty-third bottle (bottles numbered 23, 46, 69 ...)
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