Dice Puzzle(Atari 2600) FAQ
copyright 2006 by Andrew Schultz schultz.andrew@sbcglobal.net

Please do not reproduce for profit without my consent. You won't be getting 
much profit anyway, but that's not the point. This took time and effort, and 
I just had an hour or two after solving a very tough game. Please send me an 
email referring to me and this guide by name if you'd like to post it on your 
site.

**** AD SPACE ****
My website: http://www.geocities.com/SoHo/Exhibit/2762

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            OUTLINE

  1. INTRODUCTION

  2. CONTROLS

  3. WALKTHROUGH

  4. VERSIONS

  5. CREDITS

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  1. INTRODUCTION

Dice Puzzle has all the makings of a programming project. But people paid 
money for anything on the Atari 2600. It's a nice logic problem, something 
for the high school math team or introductory algorithms, but not much more. 
You have a 4x4 box of 6 sided dice. The computer mixes them up by flipping a 
row, column or diagonal by one, repeatedly, and your object is to unscramble 
them. Using some simple arithmetic this becomes a bit of a joke. It probably 
capitalized on the craze for Rubik's Cubes--and the subsequent craze by 
frustrated people for anything that looked like a Rubik's Cube that was 
easliy solvable.

  2. CONTROLS

U/D moves your cursor from left of the rows to the UL corner.
L/R moves your cursor from the UL corner to the UR corner.
The fire button pushes everything in the diagonal/row/corner up one.

Reset resets the system and start brings a new re-roll. Because the computer 
makes random moves to begin with such as you will make, and six of each move 
gets you back where you started, and moves are commutative(i.e. flip 
row/column/diagonal a, then b is the same as flipping b, then a, even if one 
is a diagonal and another is a column, or whatever) you can always get back 
to where you started.

  3. WALKTHROUGH

Let's tackle the rows and columns first in our first solution.

Label the squares as follows:

x 0 1 2 3 y
 +-------+
4|a b c d|
5|e f g h|
6|i j k l|
7|m n o p|

Now note that e+l=h+i mod 6, always, and b+c=n+o mod 6, always. Note that 
these are not affected by diagonals, so we can work on them and then address 
diagonals later. In fact, it will be trivial to.

First, set b/c and n/o to all 6's. This is not too bad. It will take 12-b-o 
or 12-c-n moves, whichever is less. You need to fire 1-2-4-7 so that 
everything turns to 6's. As good a way as any is to fire down at b(or c, 
whichever is less) until they are equal. Then fire 4 'til b=c=6 and 7 'til 
n=o=6.

Repeat for o-3-5-6 and e-h-i-l. Then you should just have two diagonals to 
take care of. Because the game is always solvable, you should just have 
diagonals of all the same number already.

If we assume that the # of rolls of 0-7 x-y are randomly distributed from 0-5 
mod 6 then we can assume you need 2.5 rolls in a best case for each of these 
to solve the puzzle. 10*2.5=25. However, because often two sets of rolls give 
the same amount of dice, in practice you can find yourself winning in less 
than 25 moves if you keep a sharp eye.

If you are very clever you may be able to influence what is on the diagonals. 
Keep in mind that you will want to keep the diagonal scores as high as 
possible. There are usually 2 ways to go about completing a 4-pack of 
numbers. Let's take an example below with b-c-n-o.

1 4


6 3

Solution 1: 1 4->6 3(increases a and d by 5)

3>6
3>6 (doesn't increase corner squares)

Solution 2:

1>4
6>3

4 4>6 6(changes a and d by 2)
3 3 > 6 6(changes m and p by 3)

Basically a/d increase by 6-b, m/p increase by 6-n
OR
a/d increase by 6-c, m/p increase by 6-o

Similarly to match e-h-i-l,
a/m increase by 6-e, d/p increase by 6-h
OR
a/m increase by 6-i, d/p increase by 6-l

That leaves 4 possibilities to calculate. Whichever leaves all your corner 
squares at their highest sum values is the one to go with. It shouldn't take 
that long to calculate, but if in doubt you can pick the way that is least 
likely to tip a corner square over a 6.

Note that we can also use reverse reasoning to match up the diagonals. 
a+f=b+e mod 6, necessarily, if we never moved the diagonals. Now each 
diagonal move adds 2 to a+f, so we can only move 0-2 times, but each of these 
moves is necessary. Repeat for c-d-g-h(c+h=d+g) and then you are in business. 
You can also check if b+k=c+j although this gets you into tricky territory. 
It may not be clear which diagonal to change although if you look into the 
position you may see that changing one diagonal may work better than changing 
the other.

End of FAQ proper

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  4. VERSIONS

1.0.0: submitted to GameFAQs 8/6/2006, complete.

  5. CREDITS

Thanks to CJayC as usual for such a great site and, though I hate to admit 
it, the people who write for more popular games so that these old school FAQs 
can be hosted for free.
Thanks to the usual GameFAQs gang. They know who they are, and you should, 
too, because they get some SERIOUS writing done. Good people too--bloomer, 
falsehead, Sashanan, Masters, Retro, Snow Dragon/Brui5ed Ego, ZoopSoul, 
BSulpher and others I forgot. OK, even Hydrophant in his current not-yet-
banned message board incarnation.
Thanks to the folks who programmed Stella, the best Atari emulator out 
there(love the save states,) and the folks at AtariAge for having information 
about every Atari game under the sun(or under the blacktop, as X million 
copies of E.T. are.)
Thanks to all the math camps and contests over the year that made a FAQ for a 
game like this a breeze even at * AM, compared to the late night problem 
sessions, anyway.