A bridge was guarded by an evil troll. The troll was very intelligent, but he was also a coward. He was afraid of anyone smarter than him. So every time anyone tried to cross the bridge, the troll would set up a test. If the traveler passed the test, he would be allowed to cross. Otherwise, the troll would eat him.
A judge named Oscar came across the bridge. The troll said, "You may only cross my bridge if you know the password." He then wrote 26 equations on a rock: A=1, B=2, and so on until Z=26.
"Today's password is the name of a woman," said the troll. "The woman's name has the same 'product' as the word JUDGE, that is, 10*21*4*7*5. It also has the same number of letters as JUDGE. However it has no letters in common with JUDGE."
"When the first and second letters in the woman's name are switched around, the letters are in alphabetical order."
"Finally," said the troll, "the woman's name does not contain the letter C because I despise the number 3."
So, what is the password? And why couldn't the troll use similar rules to create a password using the name OSCAR rather than the word JUDGE?
