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Lengthy Word (Posted on 2012-03-29) Difficulty: 3 of 5
A certain word has thirteen letters.

1) Each pair of letters below consists of one letter contained in the word and one "other" letter.

A | B  | C | D | E | F | G | H |  I  | J | L | S | Y |
V | W | Q | M | K | U | N | P | O  | R | X | T | Z |

2) When each "other" letter is put beneath each letter in the word, the "other" letters will appear in alphabetical order.

3) The word has the same number of letters in common with each of the following words:

                     FACE  QUEST  QUICK  SWITCH  WORLD

What is the word?

No Solution Yet Submitted by K Sengupta    
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Solution Solution method | Comment 3 of 4 |
In this case, the first two clues are quite powerful, as you can list all 26 letters (in order) with their pair written below. Then, the word must be written in order in the bottom line (with the other 13 letters being filler). When this is done, it looks like:


This looks mostly like a mess. Notice the letters "ABLY" at the end -- it seems likely that has to end the word if we want it to be 13 letters long. If we use those four letters, we can't use their pairs. So we can clean up the diagram.


The third clue becomes:

Suppose F was in the lengthy word, then U is not. If U is not, then Q is probably not, so C must be instead. However then FACE has at least 3 letters in the word, but QUEST can't because Q and U have been eliminated, and S/T are a pair so only one of S and T will be in the word. Since this would contradict clue 3, this means F is not in the word, and U is. Also note this means each word must have 2 or 3 letters in common with the lengthy word.



However, suppose there were 2 letters in each word. Then QUEST must have U and S or T in common, which prevents Q and E from appearing in the length word. But then C and K must appear (since Q/C and E/K are pairs), forcing QUICK to have at least 3 letters in common. Thus, each word must have 3 letters in common.

This means FACE must have A, C, and E as its letters in the lengthy word (since F is not included), and thus Q and K are excluded. This means QUICK must have I and C in the lengthy word, which means WORLD can't have O and must have R and D instead, which means M and J do not appear in the lengthy word. (Also note since I,C, and one of S/T appear in the length word, H can't appear or SWITCH would have 4 letters appear. So P must appear instead.)

Having exhausted clue 3, we can now use clue 1 and 2 to figure out the word:


Thus, it seems the word is UNPREDICTABLY

  Posted by Gamer on 2012-03-29 14:42:16
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