I looked at your post again, it seems you had a question about mining a block that had a new bitcoin transaction added to the block would change the hash
Yes
Let's say the current block that has the highest fees have 1999 transactions, the mining pool has a bunch of servers that distributes work among 100,000 S9 miners
Let's say it's a mining pool that accepts new miners open to the public and Jack Ma just put his S9 online and joined the pool, the servers now have 100,001 S9 miners to distribute the computational work
Let's say in a few seconds, a new transaction with a high fee, say $100 just got broadcasted to the the Bitcoin network, all the solo miners and all the mining pool servers will want to include this on the block on the proof of work, so now they are working on 2,000 transactions and the work is distributed among the miners
Let's say 2000 transactions is the limit for the block, and a new transaction comes in with a $200 in satoshis fees, this is a big entity, i.e. Blackrock that wants to send $200M worth of bitcoins to Coinbase custody and wants to be on the next block, all the mining pools and solo miners will want to work on this transaction but it will have to kick one of the transactions out of the block this usually is the lowest fee transaction but it doesn't have to be
So, things are dynamic in the mempool and all the miners and mining pools are constantly adjusting their Proof of Work parameters in the most efficient most profitable way
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It is just as difficult to mine a block with no transactions as it is to mine the block with 2000 transactions
It is just as difficult to mine the block static from a couple of minutes ago with 1,999 transactions as it is with the changes of adding a transaction with a $100 fee in satoshis and also the one where it had to kick out a transaction to include another transaction
The solution hash is not 1 hash that is the only hash. The solution hash for the block is the one that meets the difficulty, which is how many leading zeros in the hash and once that is met, the mining pool or solo miner will announce on the network, if accepted as a solution the rewards and fees given to the winning miner and everyone else work on the next block with the transactions that were not included in the block that had just been solved
https://buybitcoinworldwide.com/mining/#:~:text=To solve a block, miners,considered “Proof of Work!”