All right, all you puzzle people. I’ve got something that might keep you busy for a while. I’ve taken a sequence of nine binary digits (i.e., every digit is a 1 or a 0) and removed three of them six times. So now you have six six-digit sequences. Your task, should you choose to accept it, is to attempt to reconstruct the original sequence. I promise that every digit shows up at least once.
The six sequences that I’m giving you are as follows:[ul][li]011001[]100101[]101011[]100110[]101010001011[/ul]There you have it; happy puzzling![/li]
Also, if you do manage to find the answer, would you let me know how you got it? I haven’t the first clue where to begin.
I get the same sequence as Darwin’s Finch. I’ll see if I can find another. The key for me is determining what the first three digits must be, and seeing how each combination works thereafter. After eliminating several and then working with 101, I came up with the above. Now to try again…
Waitaminute Darwin’s Finch, how on Earth did you brute-force this puzzle? There are only 2^9 = 256 possible solutions, but in order to test each one you need to try at least 168 combinations of removals, probably many more. Looking at your choice of solution, did you just guess and get lucky or what?
Actually, an optimization occured to me while I was writing:
Start with a 9-digit sequence of numbers and count the number of zeroes and ones that appear. Each of the six sequences can have, at most, three fewer zeroes OR three fewer ones. Apply that test to each test sequence, and we’ll filter out a bunch of wrong solutions quickly.
Nothing spectacular. I just started from my first solution and reversed the second pair of digits; Biotop’s solution works along similar lines, with the first three pairs reversed. (I was actually working somewhat methodically by reversing individual pairs, after seeing Biotop’s solution - I figured if it worked with three pairs, it could probably work with some other combination of reversals).
