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)
From the clues given, the letters on top of the dice are P,I,N,T,A,G,E,F,R,M,L,C,H,O,Y,W. There are 16 different letters, so no letter appears twice in the 4x4 grid. To solve this puzzle, we will arrange the letters so that all the words can be formed, then flip or rotate as necessary to get C&O in a horizontal line with W in the upper lefthand corner.
PINT runs across the board. Every word with A in it is constructed such that the other letters must be on the same side of PINT that A is. This accounts for every letter except for W, so all the letters must be on one side of PINT, so we will begin by writing PINT across the bottom of the 4x4 grid.
x x x x
x x x x
x x x x
P I N T
FAINT tells us A is adjacent to I, and FRAGMENT requires E adjacent to N, so AGE must run left to right in the second row from the bottom. Also, from FRAGMENT, PALACE, and FAINT we know F, R, and L are adjacent to A. This requires there be a blank space to the left of A, so the layout must look like
x x x x
x x x x
x A G E
P I N T
From PALACE, C is adjacent to A and E, so it must be above G. From ARCHLY, R is adjacent to A and C and is therefore above A. Since L is either left of A or left and above A, ARCHLY requires H above R, L left of R (leaving F left of A), and Y in the upper left corner.
Y H x x
L R C x
F A G E
P I N T
CHORAL requires O above C, FRAGMENT requires M right of C, leaving W in the upper right corner.
Y H O W
L R C M
F A G E
P I N T
Rotating this arrangement CCW puts W in the upper lefthand corner, and it puts C and O in a horizontal line. Therefore, correct arrangement is
W M E T
O C G N
H R A I
Y L F P
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Posted by Bryan
on 2003-06-11 08:01:59 |
Great puzzle!
