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Playing Boggle
Can you score points by rebuilding the Boggle game board?
September 30, 2002
From the introduction, words are made by moving from adjacent letter to adjacent letter vertically, horizontally, or diagonally; a letter may be returned to in a word, but the same letter can't be used twice in a row. The Boggle board in the game played ended up with 16 different letters. By clue 1, the word PINT was formed in a straight line, so PINT is a row or column and goes forward or backward, up or down. We will solve the letter adjacencies first, then determine the orientation later; so one row of the board read PINT. By clue 4, FAINT was formed, so the A must be adjacent to the I in PINT. Further, the A must be followed in a line by GE (clue 1). So, the following arrangements are possible (in the first three, PINT may occur in any of the four rows):

   ....   ....   ....
   ....   ....   ....
   PINT   PINT   PINT   PINT   PINT   PINT
   AGE.   .AGE   EGA.   A...   .A..   ..A.
   ....   ....   ....   G...   .G..   ..G.
   ....   ....   ....   E...   .E..   ..E.

However, since one word formed was FRAGMENT (2), the last three arrangements are not possible; nor, since PALACE was formed (2), is the third arrangement possible. So, only the first two arrangements need further testing. Testing the first possibility, adding the word PALACE (2) must give

   ....
   ....
   PINT
   AGE.
   LC..
   ....

But, there is now no way to get FRAGMENT (2). So, the second possibility remains; and we add PALACE:

   ....
   PINT
   .AGE
   ..C.
   ....

and FRAGMENT:

   ....
   PINT
   .AGE
   ..CM
   ....

From the word COMET (5), there are two possible places for the O:

   PINT   PINT
   .AGE   .AGE
   ..CM   ..CM
   ..O.   ...O

Given the word CHORAL from clue 3, however, the second possibility is impossible, and we have

   PINT
   .AGE
   .RCM
   ..O.

From ARCHLY (5), we must have the H next to the O and under the R; while from ARCHLY and PALACE (1), the L must be next to the R and diagonal from the A. From ARCHLY and FAINT (4), we addthe F and Y to get

   PINT
   FAGE
   LRCM
   YHO.

The letter W completes the board and was in the upper left-hand corner (6), so there are two possible arrangements:

   WOHY   WMET
   MCRL   OCGN
   EGAF   HRAI
   TNIP   YLFP

However, the C to O in COMET was a horizontal move (5) and only one possibility remains and is the Boggle board solution:

   WMET
   OCGN
   HRAI
   YLFP

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