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mathmath333

  • one year ago

The letters of the word ALLAHABAD are rearranged to form new words and put in a dictionary. If the dictionary has only these words and one word on every page in alphabetical order then what is the page number on which the letter LABADALAH comes?

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{ The letters of the word ALLAHABAD are rearranged to form }\hspace{.33em}\\~\\ & \normalsize \text{ new words and put in a dictionary. If the dictionary has only}\hspace{.33em}\\~\\ & \normalsize \text{ these words and one word on every page in alphabetical}\hspace{.33em}\\~\\ & \normalsize \text{ order then what is the page number on which the letter }\hspace{.33em}\\~\\ & \normalsize \text{ LABADALAH comes? }\hspace{.33em}\\~\\ \end{align}}\)

  2. Nnesha
    • one year ago
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    sigh.

  3. Nnesha
    • one year ago
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    is that the original question or did you change some words ? just asking....

  4. mathmath333
    • one year ago
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    It is 100% genuine.

  5. Nnesha
    • one year ago
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    okay nvm.it's bank name i guess...

  6. kropot72
    • one year ago
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    The total number of pages in the book, with only one new word on each page, is given by: \[\large \frac{9!}{4!2!}=7560\ pages\]

  7. Empty
    • one year ago
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    I can never tell when there's a new one of these questions, for the longest time I just assumed they were always the same "counting question" from looking to the left haha

  8. kropot72
    • one year ago
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    The number of pages where the first letter of each new word is L is given by: 8!/4! = 1680 pages. Therefore the number of the first page where the first letter of the new word is L is 7560 - 1680 = page 5880. Now we need to find the number of pages after the word LAAAABDHL that occur until we reach the word LABADALAH.

  9. kropot72
    • one year ago
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    The number of new words beginning with LAA is given by 6!/2 = 360. Therefore the number of the first page with new words beginning with LAB is found from: 5880 + 360 + 1 = page 6241. The number of new words where the first letters are LABAA is given by 4! = 24. Therefore the number of the first page with new words beginning with LABAD is found from: 6241 + 24 +1 = page 6266.

  10. kropot72
    • one year ago
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    Page 6267 has the word LABADAAHL. Page 6268 has the word LABADAALH. PAGE 6269 has the word LABADAHAL.

  11. beginnersmind
    • one year ago
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    @Nnesha "okay nvm.it's bank name i guess..." It's a city in India with a population of over a million.

  12. mathmath333
    • one year ago
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    thnks

  13. Nnesha
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @beginnersmind @Nnesha "okay nvm.it's bank name i guess..." It's a city in India with a population of over a million. \(\color{blue}{\text{End of Quote}}\) *i guess* i just read the heading https://gyazo.com/8676ed0390348c4c7db93901200ffe25 so i thought it's a bank XD according to wikipedia it supposed to be `Ilahabad` nd then British changed to `Allahabad` dun't know why..... it pronounced like `Aallahbaad` not *bad*

  14. Nnesha
    • one year ago
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    sorry mathmath333 ,-, ...

  15. mathmath333
    • one year ago
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    I 'the monk" forgives u nesha

  16. kropot72
    • one year ago
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    You're welcome :)

  17. Nnesha
    • one year ago
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    thank u :P it's *nnesha :D :D

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