That is my name

A S H I S H \large \color{#D61F06}{\text A}\color{#3D99F6}{\text S}\color{#20A900}{\text H}\color{#CEBB00}{\text I}\color{cyan}{\text S}\color{#EC7300}{\text H}

If all the words (with or without meaning) that can be formed by the letters in my name above are written down in a dictionary such that each page contains only one word, then which page of this dictionary would contain my name?


The answer is 22.

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1 solution

Ashish Menon
May 12, 2016

The distinct letter of ASHISH are A,H,I,S arranged in ascending order.
ASHISH is of six digits.
First alphabet in dictionary occupying the first digit should be A(words starting with A). And it is so in my name ao ww proceed to the second digit. In alphabet first words starting with AH would come, but ASHISH starts with AS. So, 4 ! 2 ! \dfrac{4!}{2!} words can be formed which start with AH. Then after AH comes AI. But ASHISH starts with AS, so 4 ! 2 ! × 2 ! \dfrac{4!}{2! × 2!} start with AI. Then comes AS and ASHISH too starts with AS, so we proceed to the third digit whicb acc. ti dictionary would start with ASH first which is indeed so in my name so we proceed to the fourth alphabet. In dictionary words starting with ASHH would come first, bu my name starts with ASHI, so 2 ! 2! words start with ASHH, then comes ASHI which is indeed as in my name so we proceed to the fofth alphabet. Only H and S are left. First comes H but my name starts with ASHIS, so there is 1 ! 1! words starting with ASHIH, then comes ASHIS, which is indeed as in my name. Then then only alphabet left is H. So we put it in :- ASHISH.

So, my name would be in the 4 ! 2 ! + 4 ! 2 ! × 2 ! + 2 ! + 1 ! + 1 \dfrac{4!}{2!} + \dfrac{4!}{2! × 2!} + 2! + 1! + 1 th page = 12 + 6 + 2 + 1 + 1 = 22 12 + 6 + 2 + 1 + 1 = \boxed{22} nd page.

@Ashish Siva Can you help me solve this REALLY REALLY HARD GEOMETRY QUESTION

Jason Chrysoprase - 5 years, 1 month ago

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Sure I shall try

Ashish Menon - 5 years, 1 month ago

BTW, great problem :)

Jason Chrysoprase - 5 years, 1 month ago

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Someon changed my question :((((

Ashish Menon - 5 years, 1 month ago

I think the ans shouhd be 20th

Sahil More - 9 months, 1 week ago

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