The Secret Word

Logic Level 2

AIM        DUE        MOD        OAT        TIE \large \text{AIM} ~~~~~~~~ \text{DUE} ~~~~~~~~ \text{MOD} ~~~~~~~~ \text{OAT} ~~~~~~~~ \text{TIE}

One of the words listed above is my secret word.

If I tell you any one of the letters in my secret word, then you know the number of vowels in my secret word.

What is my secret word?

AIM OAT DUE MOD TIE

Viki Zeta by Viki Zeta , 19, India

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2 solutions

Chung Kevin
Nov 15, 2016

Observe that all of the words have 2 vowels, with the exception of MOD which has 1 vowel. Hence, the secret word cannot contain any of the letters M, O or D. The only word that satisfies this condition is TIE.

Conversely, if we're given any of the letters T, I or E, we know that the number of vowels in the secret word must be 2, since all of the words that contain that letter have 2 vowels.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

Good way of eliminating what is not possible, and then checking that what's left works!

Calvin Lin Staff - 4 years, 7 months ago
Viki Zeta
Nov 14, 2016

There are a total of 7 letters : A, I, M, D, U, E, O, T. Now think of choosing each letter and guess how many vowels you can get. To simplify our result first lets choose consonants - M, D, T.

  • M : AIM - 2 vowels, MOD - 1 vowel. Not possible .
  • D : DUE - 2 vowels, MOD - 1 vowel. Not possible .
  • T : OAT - 2 vowels, TIE - 2 vowels. Possible .

T :

  • OAT : If I say O OAT - 2 vowels, MOD - 1 vowel. Not possible
  • TIE : If I say I : AIM - 2 vowels, TIE - 2 vowels. If I say E : DUE : 2 vowels, TIE : 2 vowels. POSSIBLE .

Therefore the answer is TIE \text{TIE}

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Hm, I'm not quite sure what you're doing here, or that the solution is incomplete. Currently, you seem to be claiming that "Since T is possible, hence T must appear in the word", which isn't a valid logical step.

It would make more sense to me if you tested all the 7 letters, and then showed which letters are possible / not possible, and then found the words which only used the possible letters.

Calvin Lin Staff - 4 years, 7 months ago

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Am reducing the possibility of answer by first checking with consonants, i.e. what will happen if the letter said was a consonant

Viki Zeta - 4 years, 7 months ago

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