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The LOGIC behind the Binary Puzzle to power up Gray's Computer

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  • The LOGIC behind the Binary Puzzle to power up Gray's Computer

    I'm still working on this. I think I've figured out the Amateur level. I haven't tackled the Master level yet but I will. But first I wanted to post this for the information of anyone who might be interested.

    You start with 16 buttons arranged in a circle on the left of the screen. On the right is a list of numbers 0-15 represented in binary form where a red dot represents the binary character of 0 and a blue dot represents the character of 1. Next to each number is a symbol indicating whether or not that number is locked. The 16 buttons are all red but each one can be switched to blue by clicking on it. At the same time all the numbers are locked except for the number 0. If you switch all 16 buttons to blue all the numbers will be locked except for the number 15.

    The key to understanding what you must do to complete the puzzle is this statement that Nancy makes when you initiate the puzzle. "I need to get all of the numbers shown clockwise on the wheel using their binary code."

    That's it. That's what you have to do. You have to click buttons so you end up with a pattern of red and blue in which the four dot color combination of each number from 0-15 can be found somewhere on the wheel. If somewhere on the wheel there are four red dots in a row you have the number 0 and that number on the right will be unlocked. If you also have three red dots and a blue dot somewhere on the wheel you have the number 1 and that number on the right will be unlocked. A red, red, blue, red on the wheel will unlock number 2. Red, red, blue, blue will unlock 3.

    That's why you start the puzzle with only number 0 unlocked. All the buttons are red and you can easily find four reds together. But every other number from 1-15 requires the use of at least one blue dot. Since there are no blue buttons on the wheel they must be locked. Likewise if all the buttons are blue you can easily find four blues together. That unlocks number 15, but no other since all the other numbers require at least one red dot.

    You start with all red buttons and only number 0 is unlocked. Click a button, any button, and it turns blue. That keeps 0 unlocked and unlocks 1, 2, 4 and 8. Of course. 1 is RRRB, 2 is RRBR, 4 is RBRR and 8 is BRRR. And with only one blue button on the wheel that button is surrounded by red buttons. You need three reds in front of it to get 1, you have it. You need two reds in front and one red after to get 2, you have it. One red in front, two reds after, you've got 4. Three reds after, you've got 8.

    Several entries in the Hints give the solution to Amateur level as clicking to blue buttons 2, 3, 4, 5, 8, 10, 11, 13 on the wheel. That is quite correct.

    But really it doesn't matter what you call the buttons. You can pick a button, any button, and call it button 1. Then if you click it and then click buttons 2, 3, 4, 7, 9, 10, 12 you've completed the puzzle. Or you could click any button and call it button 15. Then you would click 16, 17, 18, 21, 23, 24, 26. If that's what you want to call the buttons. That works too.

    The important thing is not what number you assign to any button, or even what order you click them. What matters is when you get through clicking you have a pattern of B B B B R R B R B B R B R R R R. That will give you the four dot color combination of every number from 0-15 somewhere in that pattern. Just like Nancy said. You have all of the numbers shown clockwise on the wheel.

    That's Amateur level. What will I find on Master level? I don't know. I haven't tried to analyze it yet. It's got to be more complicated, otherwise the solution would be the same. So there must be some other combination of red and blue that ends up on the wheel when you're through clicking buttons. But that combination has to be related in some way to the binary number colors of 0-15. Well, I'll try to find out.

    UPDATE:

    Master Level.

    Well, that was easy. The solution is exactly the same as in the Amateur level. Elsewhere in the Hints it's been called 2, 3, 4, 5, 8, 10, 11, 13. Either level, it works. Pick any button on the wheel and call it button 1. That then defines the button immediately clockwise to it as button 2, The next button CW is 3. All the way CW around the wheel to button 16, and then you're back to button 1. Once you've assigned numbers, merely for reference purposes, you can click 2, 3, 4, 5, 8, 10, 11, 13 in any order that suits your fancy, and when you've got all eight buttons clicked you're done.
    Last edited by Demetrius; January 19th, 2020, 04:26 PM.
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