The following design is possible:
1) miner ONE (human) makes a captcha and the client app submits it to a pool server
2) miner TWO (human) gets a random captcha from a pool server and submits back the answer
3) random p2p clients (human) get both the original captcha and the answer and verify that the answer is correct
4) if the answer is correct a block is created and miners ONE and TWO get a reward
5) p2p clients also get a small reward but for just verifying (kinda transaction processing), regardless of whether the answer was correct and their intention is to keep the blockchain healthy as only then their earnings make sense
* depending on how many p2p clients verify the answer the number of confirmations limits the coin supply processing speed and security
* pool server is a p2p node in the network
* a captcha can be anything, no software will understand it
the coin should be called HumanCoin
but if miner ONE posts the captcha he just made to a forum, so miner TWO can find it and solve it effortlessly, then modified clients could do this broadcasting of solutions and later submission of answers in an automated way. Notice that these bots do not solve the captcha, they don't need to know how to solve it, just publish and resubmit the solutions. Miner ONE and TWO are the same person, or miner ONE gives the answer to miner TWO for a small % of the $.
One of the strengths of the bitcoin protocol is that an 'evil' modified client (node) has no way to cheat.