Ok, so, when I first found out about this puzzle and started looking into it earlier this year, I was initially working under the assumption that there would be some clues or patterns that could be found to help unlock the remaining wallets... But, of course, I now know what you all already knew: There are no clues or patterns, at least nothing included
intentionally by the person who created and funded these wallets...
However, I recently revisited my pattern-finding script, looking instead for any bias(es) in the data that I might be able to find (created by the pseudo-random number generator, or by assumptions built into the wallet generator's code, etc) to at least help shrink the given search spaces as much as possible, and I think I may have (possibly, maybe) found one... The problem is that even if I'm right, I just don't have the computing power to test my theory, nor the funds to buy/rent it, and won't for the foreseeable future... So I'm just going to post it here, in the hopes that, if it
is useful at all, then whoever uses this to help them open any of the remaining wallets will be generous enough to kick-back a percentage of the winnings (my BTC address is
bc1qmzud9l4aedq6h73efaj3vg3fdqhgv8w4ktq0pt)
Ok, so, my theory goes like this: I initially looked at all of the known pkeys (as decimal numbers, not hex) and calculated their location within the given puzzle's search space as a percentage, like this for Puzzle #11:
Hex: 0000000000000000000000000000000000000000000000000000000000000483
Hex as Decimal: 1155
Search Space: 1024 to 2047
Percent: (1155 - 1024) / (2047 - 1024) = 12.8%
Now, if that math is wrong, then I'm already screwed and you can give-up now
But after doing that for all the known pkeys, and looking at all the results, I didn't see any pattern, so I gave up and moved on to the next possible pattern I could think of... However, when I went back looking for a bias in the data instead of an outright pattern, I believe I
have found that certain percentages (when just looking at the whole number... so 12% for the above example, instead of 12.8%) do (seemingly) occur more often than most...
I first grouped them by the tens (so 20 for 20-29, and 30 for 30-39, etc) and here's the results:
Tens Count Percents
60 13 62,63,64,64,64,65,66,66,66,67,68,69,69
30 9 31,31,32,33,33,35,36,36,38
40 9 40,43,43,44,45,45,46,46,49
10 7 10,12,13,17,17,19,19
90 7 91,92,92,95,95,96,97
80 6 82,82,82,82,82,87
20 6 22,23,23,27,28,28
50 5 50,51,51,54,57
70 5 70,72,72,75,75
0 4 0,6,8,9
So, looking at it that way, you can see that it
seems like the 60-69% range hits way more often than the average... But even searching 10% of any given search space is still a
crap-ton of brute-forcing to do, so I kept looking and noticed that certain individual numbers show-up more often than others, so next I grouped more simply by just the whole number:
Count Percents
5 82
3 64,66
2 17,19,23,28,31,33,36,43,45,46,51,69,72,75,92,95
1 0,6,8,9,10,12,13,22,27,32,35,38,40,44,49,50,54,57,62,63,65,67,68,70,87,91,96,97
And here it appears as though the 82% range occurs way more often than any other, followed closely by 64% and 66% (which occur 3 times each)... Which could (again, theoretically) let you search only 1-3% of any given search space... But, unfortunately, that's still way too much brute-forcing for me to even attempt, given that there's no way to know which of the remaining pkeys will hit these ranges (and so you'd have to try several before finding a hit...)
...and that's assuming that this is a true bias in the data, and not just a coincidence that would even-out over time, which is the other possible way I can think of that this theory could completely fail: Maybe all the keys that could be found within the eighty-two-point-something percent range of their search space (for example) have already been found, leaving the others that have only hit once or twice so far to "catch up", statistically speaking...
Anyway, am I just an idiot, or does this make any sense to y'all...?
