Brain Teasers
The Troll Bridge 3
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?
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?
Hint
1. It is unnecessary, and even inconvenient, to multiply 10*21*4*7*5.2. This puzzle requires knowledge of women's first names.
Answer
The password is FANNY.The woman's name cannot contain G or U, so since 14 is the only other multiple of 7 to be less than or equal to 26, the name must contain two N's. Dividing by 14 twice, we get 10*3*5.
Since two of these numbers are divisible by 5, the name must contain either two letters divisible by 5 or one letter divisible by 25. It obviously cannot contain E or J. It cannot contain T because 10*3*5 is not divisible by 20. It cannot contain O because dividing 10*3*5 by 15 gives us 10, which would mean that E or J is in the name. So it must contain Y. Dividing by 25 gives us 2*3.
2*3 is one of only two pairs of numbers that multiplies to give us 6, the other being 1*6. So the remaining two letters must be either B and C or A and F. But since C is not in the password, the remaining two letters must be A and F.
Putting the five letters in order, we get AFNNY. Switching around the first two letters, we get FANNY.
The reason why the troll couldn't use similar rules to create a password using the name OSCAR is because S is the 19th letter of the alphabet, and 19 is a prime number and the only number less than or equal to 26 to be a multiple of 19.
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Comments
This was fun. The setup was a bit intimidating and may have scared many readers away, but if you give it a moment it becomes a fairly straightforward prime factor shuffling problem. I don't think you need to know women's names to solve it. The final letter sequence should be the only one that works. The biggest challenge for me was realizing I could use the letter A without changing the product, a minor hurdle.
Fun puzzle!
Fun puzzle!
Excellent puzzle. I solved it exactly as described in the answer. It took a moment to realize that the answer must include an a.
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