BC does this by letting everyone submit answers, but making it really hard (computationally intensive, aka, burn electricity) for your answer to the be the one that's accepted.
PeerCoin (to pick one) does this by making your likelihood of being The One correlate with your investment in the worth of the coin (literally how many of the coins you control). If you're the One, either your answer is accepted, or you're selected to give the answer, and then it's accepted - I'm not sure which.
You can also limit participation in your blockchain in combination with these; for example, a closed (invite-only) bitcoin would still burn electricity, but not nearly as much.
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