## Thursday, October 04, 2007

### War Soldiers

A group of 100 soldiers suffered the following injuries in a battle: 70 soldiers lost an eye, 75 lost an ear, 85 lost a leg, and 80 lost an arm.

What is the minimum number of soldiers who must have lost all 4?

1. I come up with TEN that must have all four...

2. I believe the number is higher than that. I think that at least 45 soldiers lost all 4.

3. A group of 100 soldiers suffered the following injuries in a battle: 70 soldiers lost an eye, 75 lost an ear, 85 lost a leg, and 80 lost an arm.

I swear I think I am right on this one. If 80 lost an arm, then there are 20 that didn't. If all of these 20 were the same ones that lost legs, then only 65 would have lost a leg and an arm. That leaves 35 that didn't lose both. If out of those 35 that only lost either a leg or arm, all of them lost an ear, that would leave 40 that had to have lost all three so far, leaving 60 that would have only lost 2 or fewer body parts. That means, that is all of those 60 that are left lost their eye, then that leaves 10 (70-60=10) that would have to lose all four. I worked it out in Excel and I swear it works

4. I was having a hard time figuring this one out, but you certainly convinced me. I was definitely coming at it in the wrong way.

5. You can't assume that the same 20 that lost an arm lost a leg.
25 soldiers still have ears.
30 soldiers still have eyes.
20 soldiers still have arms.
15 soldiers still have legs.
I think the answer is 14, one lower than the lowest number of soldiers that still have something.

6. The answer i believe is 70

7. It is 10.

8. There are full 310 injuries if all four lost their 70+70+70+70(ear,eye,arm,leg) then it would be 280 and remaining from 310 is 30 ..... So there would be 70 no. Of soldiers who will lost all his 4 things

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