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There is no such central server. The difficulty is adjusted using an algorithm that all the bitcoin clients implement. This looks at the generation times of the last 2,016 blocks and works out from that if difficulty needs to be higher or lower.

Since all clients implement the same algorithm, they all get the same difficulty value.

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And if some clients decide to calculate difficulty differently, it results in a block chain fork.

Could someone program up a client that "cheats"? Or is there something preventing that.

Any blocks that client produced would not match the expectations of the other clients. The difficulty being different would mean a successful hash that solves the block may not be seen as solving it by the other clients. They would reject it and your cheating client would be on its own fork.

If you could convince others to run your client then your network would get bigger. If it got >50% of the entire network then your blockchain would effectively be the main chain.

It would also have to maintain the >50% hashing power for more than 120 blocks. And even then it's not guaranteed as smaller pools could get lucky and solve more blocks than the larger rouge miner.

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