What happens when any of the nodes aren't active in a blockchain? How does the validation system work or how much time does it take then?

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If all nodes go off line, then the platform is down and thus no transactions can be completed. However, that is unlikely for a working and supported coin. If a single or a small subset of nodes go off line, then no change occurs. The time it takes for validation depends on the difficulty level of the network, the capability of the network and finally the amount of hash power from the miner.