Question

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 traveller
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 letters
because I despise the number 3."
So, what is the password? And why couldn't the troll use similar rules
create a password using the name to create a password using OSCAR rather than the word JUDGE?
​

Answer 1

hey..its ur ans:-

The password was HOE.

The only letters unique to one of the five words were D, H, P, R, and V. One of these letters must have been Al's, since he could determine the password. The only word without any of these letters is TOE. So the password could not have been TOE.

Ben knew this and now had four words to think of. The only letters unique to one word were D, E, H, P, R, T, and V. The password must have contained at least two unique letters, one for Al and the other for Ben, since they were both able to determine the password. The only word with only one of these letters was OAR. So OAR could not have been the password.

Carl knew this and now had three words to think of. The only letters unique to one word were D, E, H, O, P, T, and V. The password must have included three of these letters, since all three were able to determine the password. The only one of the three words containing three such letters was HOE, so this must have been the password.

Answer 2

(NOT HOE)

Answer:

FANNY

Step-by-step explanation:

JUDGE

= 10 * 21  * 4  * 7 * 5

= (2 * 5) * ( 3 * 7 )  * (2 * 2)  * 7  * 5

Nothing is common with judge

7 factor are 7 , 14 21   from 1 to 26

7 & 21  ( E & U used in judge)

so only 14 left

7 is twice so

14 is to be used twice

N will come twice

(2 * 5) * ( 3 * 7 )  * (2 * 2)  * 7  * 5

= (2 * 7) ( 2 * 7)  ( 2  * 3  * 5 * 5 )

C is not used in name  so 3 can not be

E is there so 5 can not use

3 * 2 = 6  F

5*5 = 25 Y

A = 1 (multiplication with 1 will not cause any issue)

FANNY