If you are not familiar with the Dice Game contact me or James Bach or Michael Bolton ( or others of the same community) and they’ll play the first round with you. It helps the players to develop their testing skills – mainly test design and managing you test data.
If you want to solve it by yourself – do not read forward.
James introduced this as very difficult one to solve. Proposed once in RST class by a student, an architect. It took James and his colleagues a lot more test data and more than few weeks to solve, which says a lot.
Well, considering the complexity of this puzzle, the first idea that came to me was that the numbers are in base 9 not base 10 as would be assumed. Look carefully, there are no number 9’s in the picture. Keeping that in mind, I noticed how some of the dice are tilted by 90 degrees. Look at the sixes and threes in the picture. Good, that could be something as well. Another thing I considered was sequence of dice, and number of dice must be calculated when trying to figure out the REAL number.Looking at the numbers in different row’s they seem to follow a certain patter, so maybe the formula for calculating the REAL number is different for different dice ?
Anyway, I have some ideas to start with, let’s see if I can figure anything out.
Hypothesis 1: ” First Dice is with face value, next similar one adds one, third similar one will add face value, etc.”
– Well this clearly does not work for 3’s and up.
New Idea :
May-be the way the REAL number is calculated uses a “mod” division or “div” ?
Hypothesis 2: “Face values are added and then “mod 4″ and then number_of_dice is added in base_9:”
1st Die : (“1” mod 4)+1 = 2 ok
2nd Die: ( “2” mod 4) +2 = 2 ok
3rd Die : (“3” mod 4) +2 = 2 not ok.
– It seems that this might lead up to something but the first system is not good enough. I continued experimenting with similar systems for a while. And then tried different systems for different dice. And then got bored. And this is clear sign for defocusing !
– Notice something off ? Good, i got the “mod” and “div” functions wrong. I found it out while writing this report from my notes. I’ll come back to it later. The moral is : Return to your test data, review and analyze, you might have mistaken or forgotten something.
May-be the face value of the die has nothing to do with it. It only indicates which formula to use ?
Hypothesis 3:”1,2,4 are always the same. The REAL number depends on the ‘number_of_dice’. The same goes for 3,6, but 5 is something weird and in base_9″
So one of the other test cases on the picture, showing dice “2 3 3 1 5” must be : 2+6+2+4=14(dec)=15(base_9)
or if we take the two 3’s and ‘1, 2’ as one group : 3+6+4=13(dec)=>14(base_9)
– Which still does not work. After trying with some more similar systems i shouted : ! DEFOCUS !
May-be it is to do with the line of dots, how many horizontal or diagonal lines there can be ? On one die or over all presented dice ? After all the guy who presented it was supposed to be an architect, and they like lines, right ? Not to mention that in the class the first solution has to do with dot patterns, that might have given him the idea. ! Some of the dice were tilted in the picture too !
After juggling the dice and counting the dots and lines every way they seemed to go I was on verge of giving up. I even tried the ‘mod’ and ‘div’ functions again. And failed.
Thinking back to RST class I returned to the wine glass. (Exercise, not drinking). Dimensions what have a used so far and what I could use:
- “sum of dots”
- “number of dice”
- “position / orientation/ lines” – which seems a bit too complicated
- Even / odd numbers
… So i returned for few hours to trying stuff that did not add up. I decided I needed more information, I cannot solve it solely on the first set of test data.
Getting more info:
I contacted James to try some tests to figure out if orientation had any relevance. I sketched dice in ‘mspaint’ and send it for him to answer with the REAL number. After few tries I sent him a die with three vertical short strips next to each other, instead of normal dotted die – to put him in a spot – and my astonishment he answered with a number : “12”
Oh the excitement ! I had discovered something. A lot more tests later i was holding lot more information. Some of the lines would give ‘error’ the others some numbers. Unfortunately, this did not lead me much closer to the real algorithm.
I will continue when I have more time to investigate the problem. Stay tuned…