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# Ann's dress' color

Posted on 2006-04-24
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Ann, Carol, Eve are friends. Ann wearing blue if only eve wearing red.  Ann and carol can wear red but not on the same day.  Carol and eve can wear blue both not on the same day.  Find Ann's dress' color?
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Question by:shilpi84

LVL 45

Assisted Solution

Hi shilpi84,

Blue

If she wears red, carol cannot wear red ... so carol must wear blue. If carol wears blue, eve has to wear red. If eve wears red, then Ann has to wear blue.

Cheers!
Sunnycoder
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LVL 30

Assisted Solution

Ann BLUE  Eve RED
Ann RED Carol RED (not same day)
Carol BLUE Eve BLUE (not same day)

If Ann wears BLUE, then Eve wears RED.  If Eve wears RED, then Carol Must wear BLUE

Since there is no restriction on the color Carol wears, and can still wear BLUE.
0

LVL 3

Accepted Solution

Total cases ar 2*2*2 = 8
Ann   Carol   Eve
1  Blue   Blue    Blue (Not Possible as 1. Ann wearing blue if only eve wearing red.  2. Carol and eve can wear blue both not on the same day.)
2  Blue   Blue    Red (POSSIBLE)
3  Blue   Red    Blue (Not Possible as Ann wearing blue if only eve wearing red.)
4  Red   Blue    Blue (Not Possible as Carol and eve can wear blue both not on the same day.)
5  Blue   Red    Red (POSSIBLE)
6  Red   Red    Blue (Not possibel as Ann and carol can wear red but not on the same day.)
7  Red   Blue    Red
8  Red   Red    Red (Not possibel as Ann and carol can wear red but not on the same day.)

Ann wearing blue if only eve wearing red.  Ann and carol can wear red but not on the same day.  Carol and eve can wear blue both not on the same day.

Case 2 and Case 5 are possible which concludes that Ann Wears BLUE

But I think case 7
Ann   - Red
Carol - Blue
Eve    - Red

Seems also possible as

Carol and eve can wear blue both not on the same day. (Condition Satisfied)
Ann and carol can wear red but not on the same day.    (Condition Satisfied)
Ann wearing blue if only eve wearing red. (Sattement is contradictory ...only eve wearing red.... means Ann including or excluding)

IF excluding then is is impossible but if we include Ann then is seems possible

0

LVL 5

Expert Comment

Green,

after all, that would seem far less complicated.
0

LVL 30

Expert Comment

cool. thank you!
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