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All the King's Wine
Your solution is flawed since on the second day you have only 9 servants left and on the third day only 8 servants.
One way is to modify it so that instead of dividing the bottles by 10 on the second day, dividing it by 9, then divided by 8 on the third day. You will need another fourth day if the bottle still cannot be found (because some of the servants drank from two bottles).
In fact the solutions for this problem in general is to divide the bottles into groups similar to a tree with n-branch, with n = 2 ... 10. However, you need to make sure that the person who died on the upper branch will not be the ones to drink bottles on the lower branches. This way, the number of servants died varied from 3 to 10 servants for n = 10 to 2.context