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## Question

Five genius friends were enjoying picnic on the occasion of New year’s day. They played a very interesting game, which employed logical thinking.

One of the friends, Ajit wrote following words, on a sheet of paper:

BEND, SOON, SEND, BOND, SINE, BIDS, NINE, NOSE, BINS, SEEN, NONE, DONE, DINE, NOON.

Then, Ajit selected a secret word from the above list and secretly distributed all four letters of this word, to the other four friends, writing one letter each on the four different pieces of paper.

[1] After this Ajit told them, "None of you can tell how many vowels the word selected by me has."

All the other four friends agreed him.

[2] Then after a brief pause, on second instance, again Ajit said, "Still no body of you can tell how many vowels the secret word has."

Again all the other four friends agreed him.

[3] Again after a brief pause, third time, Ajit told them, "Still none of you know how many vowels the secret word has."

And then, Rohit, one of the four friends, came out to say, "I know what the secret word is..!!"

So, Friends, You are required to tell What was the SECRETE WORD and how Rohit came to know the word?

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Lets say each guy prepared a list of the word of their letters. So, anyone who got 'S' will prepare a list like SOON, SEND, SINE, BIDS, NOSE, BINS, SEEN. And similarly we can have list for each of 8 letters letters used in 14 words. The number of words for each letter is: B-4, E-8, N-13, D-6, S-7, O-6, I-5.

First of all, we can easily guess that none of the guys got 'B' otherwise he would have known that there is only one vowel. But other guys were not aware of that. When Ajit asked for the first time, they became aware of that and every one omitted words with letter B. So they would have left with these many words: E-7, N-10, D-3, S-5, O-5, I-3. But each word having O now (SOON, NOSE, NONE, DONE, NOON) and having I now (SINE, NINE, DINE) has two vowels. so any guy who got it would have guessed this after first question. Since they didn't know, no one got O or I. this was evident after they answered second time affirmatively. Other guys at this point came to know that no one got O or I so they omitted those words which has O or I. they were left with these words then: E- (SEND, SEEN); N-(SEND, SEEN); D-SEND; S-(SEND, SEEN). Has anyone got D he woulds have assured of the word SEND. But, they didn't know for the third time because none of them got D and others were confused between SEND and SEEN. So, after third time, Rohit understood that none has got D and the secret word is SEEN.

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The possible words are:

BEND, SOON, SEND, BOND, SINE, BIDS, NINE, NOSE, BINS, SEEN, NONE, DONE, DINE, NOON.

Stating that no one knows how many vowels are there in the first place, means that no one got a letter B, since B-lettered word have ONLY one vowel. Thus, we can rule out all words that contain a B. The remaining words are:

SOON, SEND, SINE, NINE, NOSE, SEEN, NONE, DONE, DINE, NOON.

Still no one can guess the number of vowels, so we can rule out the O-lettered words, since all words that include at least one O, also have another vowel. The remaining words are:

SEND, SINE, NINE, SEEN, DINE.

Again, no one can guess how many vowels are there, therefore, we can exclude the I-lettered words, since those which contain an I always have 2 vowels. The remaining words are:

SEND, SEEN.

Then, the friend who has a letter D speaks up his mind!!! The secret word is SEND.

aaa

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I think it is

SEND.

The first time the Ajit says you cannot determine the vowels, eliminates all the words with B in them (all "B" words have 1 vowel)

The second time eliminates all the words with O in them (all remaining "O" words have 2 vowels)

The third time eliminates all the I words (all remaining "i" words have 1 vowel)

this leaves only one word: SEND

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@ jagdmc and @preflop: Why those guys need two different step to eliminate words with vowels 'O' and 'I'? Both of these can be eliminated after Ajit asked for the second time - all such words has exactly two vowels. No need to wait for him to ask for third time. I assume they are smart enough and they know that vowels are : A, E, I, O, U.

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Send

. The first time they were asked, they ruled out all words containing B as all words with B have only 1 vowel then at the next question , they rule out all the words containing O and I , as all words containing them have 2 vowels. So what was left was send and seen, and when asked the 3rd time, the one holding D-shouted out the answer.

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The original words were :BEND SOON SEND BOND SINE BIDS NINE NOSE BINS SEEN NONE DONE DINE NOON

Stage 1: After dealing out letters of one of the words, Ajit says : No one knows how many vowels in the chosen word.

Now if any of the friends had received the letter B then this would not be true. Because all words containing B have only ONE vowel.

So Remove the words with B and then we are left with:

SOON SEND SINE NINE NOSE SEEN NONE DONE DINE NOON (note that only one word has ONE vowel, rest all have TWO)

Stage 2:Again Ajit says "no one knows how many vowels in chosen word"

in this reduced set notice that all words with O or I have two vowels each. So if anyone had an O or an I, Ajit would have been wrong. So no one had an O or an I and so we can also further drop all the words with an O or an I. That would leave :

SEND SEEN

Now at this stage if anyone had a D - he would have known what the chosen word was. So that meant each of 4 friends had letters S, E, N among themselves.

Also at this point the 4 wise friends (supposing each exactly knew how long it would take the others to figure out the above), after a wait could have concluded that none had D and so the word would have been SEEN. Perhaps they were keeping quiet because they were not asked OR they wanted the confirmation to come from Ajit - which he provided with his next statement

Stage 3: Ajit who knew that choice had shortened to SEND and SEEN, stated again "none knows how many vowels". This would hold true if the friends had only the letters S,E,N among themselves.

This sealed the answer to SEEN. In fact all of the friends - no mater what letter they were holding would have come to the conclusion. It is just that Rohit was the quicker and responded or maybe he was impatient or bored with the manner in which Ajit was dragging the game

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I think it is

SEND.

The first time the Ajit says you cannot determine the vowels, eliminates all the words with B in them (all "B" words have 1 vowel)

The second time eliminates all the words with O in them (all remaining "O" words have 2 vowels)

The third time eliminates all the I words (all remaining "i" words have 1 vowel)

this leaves only one word: SEND

Mmmmmm...

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The original words were :BEND SOON SEND BOND SINE BIDS NINE NOSE BINS SEEN NONE DONE DINE NOON

Stage 1: After dealing out letters of one of the words, Ajit says : No one knows how many vowels in the chosen word.

Now if any of the friends had received the letter B then this would not be true. Because all words containing B have only ONE vowel.

So Remove the words with B and then we are left with:

SOON SEND SINE NINE NOSE SEEN NONE DONE DINE NOON (note that only one word has ONE vowel, rest all have TWO)

Stage 2:Again Ajit says "no one knows how many vowels in chosen word"

in this reduced set notice that all words with O or I have two vowels each. So if anyone had an O or an I, Ajit would have been wrong. So no one had an O or an I and so we can also further drop all the words with an O or an I. That would leave :

SEND SEEN

Now at this stage if anyone had a D - he would have known what the chosen word was. So that meant each of 4 friends had letters S, E, N among themselves.

Also at this point the 4 wise friends (supposing each exactly knew how long it would take the others to figure out the above), after a wait could have concluded that none had D and so the word would have been SEEN. Perhaps they were keeping quiet because they were not asked OR they wanted the confirmation to come from Ajit - which he provided with his next statement

Stage 3: Ajit who knew that choice had shortened to SEND and SEEN, stated again "none knows how many vowels". This would hold true if the friends had only the letters S,E,N among themselves.

This sealed the answer to SEEN. In fact all of the friends - no mater what letter they were holding would have come to the conclusion. It is just that Rohit was the quicker and responded or maybe he was impatient or bored with the manner in which Ajit was dragging the game

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This is the answer I was looking for....!

Thanks...!

Edited by bhramarraj

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