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Deploying mobile edge computing (MEC) server in the mobile blockchain-enabled Internet of things (IoT) system is a promising approach to improve the system performance, however, it imposes a significant challenge on the trust of MEC server. To address this problem, we first propose an untrusted MEC proof of work scheme in mobile blockchain network where plenty of nonce hash computing demands can be offloaded to MEC server. Then, we design a nonce ordering algorithm for this scheme to provide fairer computing resource allocation for all mobile IoT devices/users. Specifically, we formulate the user's nonce selection strategy as a non-cooperative game, where the utilities of individual user are maximized in the untrusted MEC-aided mobile blockchain network. We also prove the existence of Nash equilibrium and analyze that the cooperation behavior is unsuitable for the blockchain-enabled IoT devices by using the repeated game. Finally, we design the blockchain's difficulty adjustment mechanism to ensure stable block times during a long period of time.