PROBLEM:
 Melissa and Jessica were working on the computer along with their friends Sandy and Nicole.  Suddenly, I heard a crash and then lots of shouts.  I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass!  Sandy and Jessica spoke almost at the same time:

Jessica saying, "It wasn't me!"
Sandy saying, "It was Nicole!"
Melissa yelled, "No, it was Sandy!"
With a pretty straight face Nicole said, "Sandy's a liar."

Only one of them was telling the truth, so who knocked over the monitor?
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SOLUTION:
Nicole was telling the truth; Jessica broke the monitor.

If only 1 of the 4 was telling the truth, that means that the other 3 were lying.  By using deductive reasoning, one would conclude that the only possibility with the presented facts is that Jessica was lying when she said, "It wasn't me," Sandy was lying when she said, "It was Nicole," and Melissa also lied when she said, "No, it was Sandy."  This leaves Nicole as the truth-teller, revealing Jessica as the culprit, having stated a direct lie when she said "It wasn't me!"