Password I know -> hash function (probably with millions or billions of iterations) -> Twitter password that I don't know.
Not peeking at the Twitter password is a non-issue, people don't generally memorize the output of hash functions, even if they wanted to, they are a long string of random characters.
Here's an example: the SHA256 hash of your username is 328BFB7DEAB24355A7A0D2377AB8DEF70D8DECF968E90AA507D590ACDD25A7AC if you were to then hash 328BFB7DEAB24355A7A0D2377AB8DEF70D8DECF968E90AA507D590ACDD25A7AC you'd get 227D82D075605DE042164082145FC7D296DF20C4BAAA2834B5541182C0D13051. Hash that and get 2062A298907588A3045EE89D9C366C64097924BC50F48981CF4A736B9BB093DF. Now repeat that process a billion or so times and you'll calculate your Twitter password.
This is a really great idea, it's literally impossible to overcome the restriction.
Not peeking at the Twitter password is a non-issue, people don't generally memorize the output of hash functions, even if they wanted to, they are a long string of random characters.
Here's an example: the SHA256 hash of your username is 328BFB7DEAB24355A7A0D2377AB8DEF70D8DECF968E90AA507D590ACDD25A7AC if you were to then hash 328BFB7DEAB24355A7A0D2377AB8DEF70D8DECF968E90AA507D590ACDD25A7AC you'd get 227D82D075605DE042164082145FC7D296DF20C4BAAA2834B5541182C0D13051. Hash that and get 2062A298907588A3045EE89D9C366C64097924BC50F48981CF4A736B9BB093DF. Now repeat that process a billion or so times and you'll calculate your Twitter password.
This is a really great idea, it's literally impossible to overcome the restriction.