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So I wrote down my mnemonic on a piece of paper and somehow the last 2 words got ripped off and I cannot find where it went. I do have 10 out of the 12 word phrase still (along with the order, they are 1-10), along with the last address that coins were sent to on it.

My question, is there a way to automate finding the last 2 words? I found various examples online for finding 1 out of 12 but nothing about situations with 2 out of 12 missing. Given that theres only 2048 words in the dictionary for it and each word in the mnemonic can only use certain ones from this dictionary, I'd presume this wouldn't be too difficult of a task. Preferably, Id like to find a way to not only generate the phrases but also check them for a balance in the blockchain if possible. Anyone know how I should go about this given what I have?

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There do exist tools for this sort of situation.

For example btcrecover

btcrecover is an open source Bitcoin wallet password and seed recovery tool. It is designed for the case where you already know most of your password or seed, but need assistance in trying different possible combinations.

I don't know if they work or just steal your money (so I'd only use downloadable tools that can be run on a disconnected PC).

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