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15 Aug 2003, 05:56
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hi guys
i don't know how you express it in english, but translated directly from russian it sounds like 'logical proposition problems'
.
here is an example:
we have four students: 1, 2, 3, 4. determine how many of students passed the exam, if it is known that:
1. if 1 passed, then 2 also passed
2. if 2 passed, then 3 also passed or 1 failed
3. if 4 failed, then 1 passed and 3 failed
4. if 4 passed, then 1 passed.
first i wanted to think about this problem in terms of combination or permutation
, but i am sure it has its own ways of solution.
regards
i don't know how you express it in english, but translated directly from russian it sounds like 'logical proposition problems'
.
here is an example:
we have four students: 1, 2, 3, 4. determine how many of students passed the exam, if it is known that:
1. if 1 passed, then 2 also passed
2. if 2 passed, then 3 also passed or 1 failed
3. if 4 failed, then 1 passed and 3 failed
4. if 4 passed, then 1 passed.
first i wanted to think about this problem in terms of combination or permutation
, but i am sure it has its own ways of solution.
regards
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15 Aug 2003, 06:10
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They all Passed
Look at items 3 and 4.
#3. if 4 failed, then 1 passed and 3 failed
#4. if 4 passed, then 1 passed.
No matter what happens to 4, 1 passes, so 1 must pass...so lets start there.
Ok, so looking at item 1, #1. if 1 passed, then 2 also passed.
So now we know that both 1 and 2 passed.
Now, #2. if 2 passed, then 3 also passed or 1 failed. Well, we know 1 can't fail, so student 3 must pass as well.
Now #3 cannot result in student 4 failing, because that would require student 3 to fail, so student 4 must pass as well.
Look at items 3 and 4.
#3. if 4 failed, then 1 passed and 3 failed
#4. if 4 passed, then 1 passed.
No matter what happens to 4, 1 passes, so 1 must pass...so lets start there.
Ok, so looking at item 1, #1. if 1 passed, then 2 also passed.
So now we know that both 1 and 2 passed.
Now, #2. if 2 passed, then 3 also passed or 1 failed. Well, we know 1 can't fail, so student 3 must pass as well.
Now #3 cannot result in student 4 failing, because that would require student 3 to fail, so student 4 must pass as well.
