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| Mind Boggling (Posted on 2003-06-11) |
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In the popular game of Boggle, each of 16 dice has six different letters (QU substitutes for a single letter on one cube face) on it. The dice are shaken and fall into a 4x4 square, so that one letter on each cube shows. Players have three minutes to form as many words of length three or longer by moving from letter to adjacent letter either vertically, horizontally, or diagonally. In this game, players may return to a letter in forming a word but may not pause on a letter. Given the sample board:
F B U P
T M E O
R S H I
E T B W
possible words are POEM, PESTER, HOPE, THEME, and RESETS, but not MESS.
In a recent game of Boggle, Chad and his dad formed the words given in the clues below, as well as many others. The following observations were made:
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Both Chad and his dad got the words AGE and PINT, each of which showed up on the board in a straight line.
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Chad scored big points by making FRAGMENT and PALACE, neither of which his father had on this final word list.
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Dad scored points with CHORAL, which Chad didn't see.
Both players anagrammed FAINT and ARCHLY from the board.
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Both formed COMET, starting with a horizontal move from C to O.
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The letter W was in the upper lefthand corner of the 4x4 square.
Reconstruct the arrangement of the top dice letters that showed on their game board.
(puzzle originally from www.allstarpuzzles.com)
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Submitted by DJ
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Rating: 4.1429 (21 votes)
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Solution:
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(Hide)
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W M E T
O C G N
H R A I
Y L F P
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 upper three rows):
· · · · · · · · · · · ·
· · · · · · · · · · · ·
P I N T P I N T P I N T
A G E · · A G E E G A ·
· · · · · · · · · · · ·
· · · · · · · · · · · ·
P I N T P I N T P I N T
A · · · · A · · · · A ·
G · · · · G · · · · G ·
E · · · · E · · · · E ·
However, since one word formed was FRAGMENT (2), the E must be adjacent to both G and N, and the last four arrangements are not possible.
So, only the first two arrangements need further testing.
One of the words formed was PALACE (2), which means the A must be adjacent to the P, as well as the G in FRAGMENT.
Testing the first possibility above, and adding the word PALACE (2) must give:
· · · ·
· · · ·
P I N T
A G E ·
L C · ·
· · · ·
But, there is now no way to get FRAGMENT. So, the second possibility remains; and we add PALACE:
· · · ·
P I N T
· A G E
· · C ·
· · · ·
where the L may be in any of the three remaining spaces next to the A.
Add FRAGMENT:
· · · ·
P I N T
· A G E
· · C M
· · · ·
where the R may also be in any of three spaces (with, of course, the F adjacent to that).
From the word COMET (5), there are two possible places for the O (next to both C and M):
P I N T P I N T
· A G E · A G E
· · C M · · C M
· · O · · · · O
Given the word CHORAL (3), however, the second possibility is impossible, and we have:
P I N T
· A G E
· R C M
· · O ·
From ARCHLY (5), we must have the H next to the O and under the R:
P I N T
· A G E
· R C M
· H O ·
To form ARCHLY, the L must be next to the H. Recall that from the word PALACE, the L must also be next to the A. That leaves only one place for it:
P I N T
· A G E
L R C M
· H O ·
From FAINT(4), the F must be next to the A, while the Y in ARCHLY is next to the L. Filling in those letters:
P I N T
F A G E
L R C M
Y H O ·
The letter W completes the board, but it must be in the upper left-hand corner (6), so there are two possible arrangements the board can be rotated/reflected into:
W O H Y W M E T
M C R L O C G N
E G A F H R A I
T N I P Y L F P
However, the C to O in COMET was a horizontal move (5), and only one of these arrangements fits that. Thus, the solution is:
W M E T
O C G N
H R A I
Y L F P
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