Re: solve key 66 67 Puzzle how to avoid double spends the tx?
Some words from satoshi himself while undercover. 
There's simply no feasible way to withdraw the funds on lower end puzzles like #66. It will be snatched up by bots. Not maybe, but it's 100% guaranteed. There will be hundreds of withdrawal transactions with varying fees all battling each other. You will simply be left in the dust.
It's a fundamental flaw in this puzzle that was originally aimed to bring the community together and try to solve the puzzle. The puzzle creator did not think much about the puzzle, and this is proof of it.
The only way the original solver will get the funds of puzzle #66 is if they can prove to be in possession of the private keys directly to the puzzle creator. The puzzle creator then withdraws the funds at a 6BTC fee (they can afford it) to your address.
It's a fundamental flaw in this puzzle that was originally aimed to bring the community together and try to solve the puzzle. The puzzle creator did not think much about the puzzle, and this is proof of it.
The only way the original solver will get the funds of puzzle #66 is if they can prove to be in possession of the private keys directly to the puzzle creator. The puzzle creator then withdraws the funds at a 6BTC fee (they can afford it) to your address.
no doubt on that!
the speed now is crazy imagine
how to reach the creator? his last appear here 2019?
i believe this the only guaranteed way by giving a proof te the creator that you hit the private key and let him transfer to you
Sadly... the moment a lucky person finds the private key to puzzle 66, and post the transaction using the private key found,
the transaction itself will reveal the public key that it contains.
Right now the public key is not known (only the hash is known), the only way to solve the puzzle is guessing every possible private key,
calculate the public key, sha256 hash, and the ripemd 160.
Then compare each value to the already known hash value of the public key. There is no way to use Big Step,
Little Step algorithm or to use Pollard's Kangaroo method without knowing the public key in advance.
When the public key is revealed, then the puzzle 66 could be solved in less than one second using a normal computer with BSLS.
If you precompute a big enough database, let´s say 2^41 public key coordinates, you will only need to calculate about 8 million more points (2^23),
and solve the puzzle.
A RTX 1650 can get about 300 million keys/second so the puzzle will be effectively 100% sure, as you say, snatched by the bots.
If you post the transaction, with a very big transaction fee (6btc), all the money will go to the mining pool instead.
How will it work if many bots spend from the same address, all with very high fees?