Circuit Troubleshooting: Finding Correct States of Diodes

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seang
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Today in class we learned about diodes. Our prof explained to us that the only manual way to find the correct states of the diodes is guess and check. Each time, we ended with one correct circuit; that is Kirchoff's laws coincided with the diode constraints.

Now I'm doing this circuit on my own, and I'm finding that there are 2 combinations which fulfill Kirchoff's laws. Is this possible? or must I be making a mistake somewhere?

The circuit is simple really. DC sources resistors and diodes.
 
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Take a look at the http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Diodes/Diode1.html" and see if it helps answer your question.

Regards
 
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