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Playing Boggle Again
Can you solve the letter arrangement of the Boggle game board?
April 26, 2004
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: ABEFGILMNOPRSTUY. By clue 5, in forming the word BEST, Chad made two consecutive horizontal moves; so he either went B-E-S in a straight line or E-S-T. However, from the word OFTEN in clue 2, the E and T must also touch, which they cannot do in the second case. We will solve the letter adjacencies first, then determine the orientation later; so we put these letters on the Boggle board arbitrarily as follows:
   BES   BES
   .T.   ..T

By clue 2, the N must be adjacent to both the T (ANT) and E (OFTEN); the N must also touch the S (SNAG in clue 1). The N must therefore fit in our arbitrary arrangement as follows:

   BES   BES
   .TN   .NT

Given the word SLIT (1) and the first of our two possible arrangements, we would have:

   BES.
   .TNL
   ..I.

However, there is no way to form SULTAN in clue 1. So, our second arrangement from above is the only one possible:

   BES
   .NT

From SULTAN (1), the A must be adjacent to both N and T:

   BES   BES
   .NT   .NT
   .A.   ..A

However, since the L must touch the S in SLIT (1) and touch the A in LAMP (3), there is no way the first arrangement can work; and the L must be added as

   BES.
   .NTL
   ..A.

From SULTAN (1),

   BESU
   .NTL
   ..A.

SLIT (1),

   BESU
   .NTL
   ..AI

and OFTEN (2) we get

   BESU
   .NTL
   .FAI

Since the G in SNAG (1) must go below A in what is the 4th row, the Y and R in RYE in clue 4 fill out the other three rows:

   BESU
   YNTL
   RFAI

There are three ways that the G in SNAG (1) can fit:

   BESU   BESU   BESU
   YNTL   YNTL   YNTL
   RFAI   RFAI   RFAI
   .G..   ..G.   ...G

Given the first possibility, the M and P in LAMP (3) would have to fit in to the right of the G and the O in OFTEN (2) to the left--but MOAT (3) cannot be made. Trying the second arrangement, M and P from LAMP would be to the left of G--but there would be no way to make OFTEN. So the third arrangement remains. We try all arrangements of the M and P from LAMP with O from OFTEN:

   BESU   BESU   BESU
   YNTL   YNTL   YNTL
   RFAI   RFAI   RFAI
   OPMG   OMPG   PMOG

Only the third one allows MOAT (3) to be made. We now test the various alternative orientations:

  BESU  USEB  BYRP  PRYB
  YNTL  LTNY  ENFM  MFNE
  RFAI  IAFR  STAO  OATS
  PMOG  GOMP  ULIG  GILU

  PMOG  GOMP  ULIG  GILU
  RFAI  IAFR  STAO  OATS
  YNTL  LTNY  ENFM  MFNE
  BESU  USEB  BYRP  PRYB

By clue 4, RYE was partly formed by an upper left-to-lower right diagonal move, so only two of the arrangements are possible:

  PRYB  PMOG
  MFNE  RFAI
  OATS  YNTL
  GILU  BESU

However, by clue 5, B wasn't in the upper-right-hand corner. The Boggle board was as follows:

  PMOG
  RFAI
  YNTL
  BESU

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