Exploding Dots!
When I was a young child I invented a machine. And this machine was nothing more than a row of boxes that extends as far to the left as I could ever desire. I called this machine a and one would work this machine by placing dots into the rightmost box. Placing one dot in into the machine doesn’t do much. It stays as one dot. But in placing two dots into the machine, something exciting happens: Two dots in a box explode– kapow!–and produce one dot one place to the left.
What is the code for 50?
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1 solution
The 50 dots in the first box on the right all explode into 25 dots in the next box. "0" is the rightmost digit. 24 dots explode into 12 dots in the next box and "1" left over, giving "10". Similarly the 12 turn into 6 in the next, and 3 in the next, so we now have "0010". Finally the 2 of the 3 become 1 dot in the leftmost box and 1 dot remaining behind, giving 1 1 0 0 1 0 . Interestingly, the machine boxes are copying binary addition rules: 0 + 1 = 1 , 1 + 1 = 1 0 , 1 + 1 + 1 = 1 1 which is why the answer is the binary representation of 50.