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ANSWER: At a minimum, 10% of the soldier have lost all four body parts.

EXPLANATION: Assume for the sake of simplicity that there are 100 soldiers. This would mean that there were a total of 310 injuries (70 + 75 + 80 + 85). The scenario with the minimum percentage of soldiers having lost all four body parts will be the one where the injuries are the most evenly spread across all soldiers. For 100 soldiers, that would be 3.1 injuries per soldier which means all soldiers would have lost at least three body parts. If all soldiers suffered three injuries, that would make a total of 300 injuries. Since there are 310 injuries, we know that at a minimum, 10 soldiers (10%) have lost four body parts (to account for 310 injuries).

Lewis Carroll, author of Alice in Wonderland created this riddle.