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Homework Help: Number Box Please help me figure out

  1. Mar 2, 2005 #1
    Hi everyone-

    I'm trying to figure out this puzzle that has to with numbers inside a 20x20 square.

    After 1000 cycles, the square will always contain a 10x10 square in the upper left hand corner of all 0's, which will not change. My job is to find out what is happening to all the numbers, and why they do what they are doing. You are allowed to enter any number you wish into the cycle processor.

    Hopefully someone can help me come up with ideas, or even provide me with some hints as to what they think is happening. I've looked over this for hours, and can't figure it out, but that is probably because I'm bad with numbers! This assignment is for an Informatics class. Please someone help me out! Thanks so much!

    Here is the website address: http://informatics.indiana.edu/rocha/whitebox/WhiteBoxDigits.html

    or the color version: http://informatics.indiana.edu/rocha/whitebox/WhiteBox.html
    Last edited: Mar 2, 2005
  2. jcsd
  3. Mar 2, 2005 #2


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    OK, at first glance.

    I will make one assumption:
    - the actual colours and the actual numbers (except perhaps zero and black) are arbitrary. i.e it has nothing to do with the value of the number or the order of the colour. The numbers might as well be letters (at least for now).

    Why? Because the colour box must be solvable without numbers. If we need to resort to numbers to solve it, then we're just using the Number Box, and the Colour Box is a merely red herring.

    Ok, some deductions:
    The upper corner is exactly 1/4th of the entire area. I can see three other identically-shaped areas. My intuition tells me that this box is divided into four smaller 10x10 boxes for a reason. I would suspect that the states of these four boxes are related.

    We can set up some notation.
    Four 10x10 boxes:
    A B
    C D
    Each contains 100 squares in a grid
    We can uniquely identify any cell as a 10x10 within its box.

    Thus, the very upper left cell is labelled A0,0
    The cell in the 10th column and 10th row is the lower right corner of Box A, and is labelled A9,9.
    The very lower right cell is labelled D9,9.

    I suspect that the colour of A0,0 is dependent on the states of B0,0 , C0,0 and D0,0.

    I also suspect there's a relationship with its neighbours, since the patern grows from one corner, not randomly.

    I'll dwell some more. Does that help you out? Or have you already gotten that far?
  4. Mar 2, 2005 #3


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    BTW, what course is this for? Programming? Logic? Deductive reasoning?
  5. Mar 2, 2005 #4


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    - Merely covering the browser window with another window causes all the colours and numbers to alter.
    - The alterations are not linear (eg. multiple blues covered and then unveiled will not reveal multiple pinks or multiple reds, but multiple different colours)
    - Merely covering part of the box has the same effect. In fact, you can cover only part of a cell and upon uncovering, it will partially have a different colour.

    These observations support the theory that the actual cell values are arbitrary, and that only the relationship between cells is relevant.
  6. Mar 2, 2005 #5
    Somewhat, I found the same ideas as you did. I figured it had to do with a relationship between the 4 10x10 squares. I tried processing the box to a total of 1000 cycles multiple times, printed the results out, and highlighted all of the zeros in the total area. After each result, I received different numbers of 0's. So obviously, this isn't a factor.

    You said that the numbers are related with its neighbors since the pattern grows from one corner, not randomly. What do you mean by this?

    I guess the main thing I'm trying to figure out now is why the numbers turn to 0's in the top left 10x10 box. And when these numbers all turn to 0's, where the other numbers are going, and why?

    This assignment is for inductive modeling. Has to do with information (informatics), although I really don't see the point.
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