Try This Logical Question: Find the Rank of "Ought" & "Tough" in a Dictionary

[gauravkukreja]

Try out this problem

The letters of the word ought are rearranged to form new words irrespective of the meanings. The words were later compiled in a dictionary where they were arranged alphabetically. Find the rank of the word ought in the dictionary. Hence also find the rank of the word tough in it.

 

[gerben]

I think it is this, in white (select to view)
ought --> 66, tough --> 88

 

[Gokul43201]

gerben, I think you want to add 1 to both those numbers...

 

[gerben]

Gokul43201, yes I do

 

[bjr_jyd15]

explain

can someone explain this question to me? i know it has been solved but i'd like to know how the answer was came about.

thanks

 

[Gokul43201]

There's a partial hint here.

 

[The Bob]

There's a partial hint here.

Still don't get it.

The Bob (2004 ©)

 

[Galileo]

Alphabetical order: g,h,o,t,u.
"o" comes is the third in the list, so there are 2*4! entries before it.

 

[tribdog]

shouldn't the words be actual words? it's to easy to rearrange the letters into nonsense. you could say rearrange the numbers in 12345 into every possible combination then tell me where 12354 is in your list.

 

[gauravkukreja]

If I can help,
The alphabetical order of the letters is G,H,O,T,U
In the firt place,Words with O as the first letter will start after 2*4! words, 4! for G and H.
In the second place, U will start after 3*3! words,3! each for G,H,T
After this Alphabetically the next word will be ought.
So the rank of ought will be 2*4! + 3*3! + 1 = 67
Simillarly For tough.