battle-field

Number Theory Level 3

In a battle, 70% of the combatants lost one eye, 80% lost one leg, 85% lost one ear, and 90% lost one arm. If some fraction f f of the combatants lost all four of these body parts, what is the minimum value of f f ?


The answer is 25.

Deepankar Singh by Deepankar Singh , 23, India

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3 solutions

Venture Hi
Mar 15, 2014

30 did not lose an eye, 20 did not lose one leg, 15 did not lose an ear, and 10 did not lose an arm. Therefore, a total of 75 people did not lose at least one of these appendages. 100-75= all those that lost 4 appendages.

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100-(100-70)-(100-80)-(100-85)-(100-90)=25!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sahil Gohan
Mar 30, 2014

let total number of people be 100. 70 people lost a eye, 80 people lost a leg, 85 people lost a ear,90 people lost a arm. therefore 325 people lost atleast one thing.

now start dividing 325 things among 100 people and youwill see 25 remain. Therefore these will get divided among people who have lost all 4 parts...hence 25

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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