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

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Discussion Overview

The discussion revolves around a logical problem involving the arrangement of the letters in the words "ought" and "tough" to determine their ranks in an alphabetically ordered list of all possible permutations. The scope includes mathematical reasoning and combinatorial analysis.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Homework-related

Main Points Raised

  • One participant presents a solution claiming the ranks of "ought" and "tough" are 66 and 88, respectively.
  • Another participant suggests that an adjustment of +1 should be made to both ranks.
  • A request for an explanation of the solution process is made, indicating a desire for clarification on how the ranks were determined.
  • One participant provides a breakdown of the alphabetical order of the letters and explains how to calculate the rank of "ought" based on the positions of the letters.
  • Concerns are raised about the validity of using nonsensical words for the arrangement, suggesting that only actual words should be considered.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using nonsensical permutations, and there is no consensus on the final ranks of the words as adjustments are suggested. The explanation of the rank calculation remains partially understood by some participants.

Contextual Notes

Some assumptions about the arrangement process and the definitions of valid words are not fully articulated, leading to potential ambiguity in the discussion.

gauravkukreja
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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.
 
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I think it is this, in white (select to view)
ought --> 66, tough --> 88 [/color]
 
gerben, I think you want to add 1 to both those numbers...
 
Gokul43201, yes I do
 
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
 
There's a partial hint here.
 
Gokul43201 said:
There's a partial hint here.
Still don't get it.

The Bob (2004 ©)
 
Alphabetical order: g,h,o,t,u.
"o" comes is the third in the list, so there are 2*4! entries before it.
 
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.
 
  • #10
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.
 

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