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:

1. Both Chad and his dad got the words AGE and PINT, each of which showed up on the board in a straight line.
2. Chad scored big points by making FRAGMENT and PALACE, neither of which his father had on this final word list.
3. Dad scored points with CHORAL, which Chad didn't see. Both players anagrammed FAINT and ARCHLY from the board.
4. Both formed COMET, starting with a horizontal move from C to O.
5. 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)

It took me all day (off and on, of course--gotta make a living), and I danced around it for hours. I finally used excel to track all my trials just so I coould see the one step I KEPT forgetting grrrr.

Anyway, the solution lies on three key points, that Pint and Age are straight lines, that CO is a horizontal connection (so it could also be OC) And that the C MUST be placed between the A and G adjacent to 'AGE.' (because of the need to spell 'Palace'). Then, looking at all of the listed words, we determine that the A must be surrounded with G,L,R,I,C,F,P in some order. What this tells us is that the A can't be on an edge because there wouldn't be enough squares; Which through investigation also tells us that 'PINT' can't be diagonal because that would force the A onto an edge (the A and P have to connect for 'Palace.'). So we basically have the following starting block

P I N T or P I N T
A G E A G E
C O C
O
depending on which way it is rotated (BTW, we know 'AGE and 'PINT' have to be adjacent because of 'PALACE' and 'COMET'. We also know that the M has to be in contact with both the O and the E, and that the O,M,H,Y can't be in contact with the A (because we've already used up our one "useless" contact with the A on the N. After that its very simple trial and error, rotating the starting configuration. Since 'PINT' can only fit on two edges (either forward or backward) we only have four possible starting points and the rest is easy (unless, like me you KEEP forgetting one arrangement--the CORRECT one).

W M E T
O C G N
H R A I
Y L F P

Posted by Jim C on 2003-06-11 11:09:27