Can miners freely choose the order of transactions within a block or are there any restrictions like the transactions need to be sorted by gas price?

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For the most part. The only stipulation is that transactions from the same address must be executed by ascending nonce - e.g. if I send 2 transactions, one with nonce 3 and one with nonce 4, the miner must order the nonce 3 tx before the nonce 4 tx.

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