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Once again, our post-doctoral protagonist Dr. Green faces an interesting challenge to her daily routine. This time the lab's precision electronic balance has gone on the fritz. And she needs to quickly determine which of her knockout mice is exhibiting an obesity-related gene. In this case, only 1 of the 27 mice in the colony is actually exhibiting the phenotype of increased body weight. By chance, or perhaps because of her phenomenal experimental technique, the remaining 26 mice are nearly the same weight. Dr. Green was able to rummage through a storage room and locate a classic 2-pan balance (i.e. with opposing pans in which two objects' weights can be directly compared). What are the fewest rounds of measurements required to exactly determine the obese mouse without relying upon luck?

For example - if there were 8 mice you might say 3 rounds (first, 4 mice against 4 mice, then take the heavier group and divide into groups of 2 to be measured, and finally take the remaining 2 and compare them directly to determine the heaviest mouse).