Since from what LoyceV described, your game / puzzle doesn't seem to involve any incentivized posting on Bitcointalk, you (or whoever you've designated) should just post a thread about your puzzle in either Bounties (Altcoins) or Service Discussion (Altcoins). If you're uneasy about breaking the forum's rules, read through the stickied threads in whichever board you intend to post in. If you're still uneasy, read through https://bitcointalk.org/index.php?topic=703657.0 if you haven't already. If you're still not sure if something you want to post is a-OK with the rules, PM me the contents of your thread and I'll glance over it.

When it comes to harsh punishments for single offenses, the main 2 are plagiarism (permanent ban for most users; long temp ban + even longer sig ban for reputable users) and on-forum altcoin giveaways (temp ban for 7-30 days). If you're neither plagiarizing nor incentivizing users to post posts in one or several specific Bitcointalk threads, you're most likely in the clear (bonus points if you've read through and understand all the rules listed in https://bitcointalk.org/index.php?topic=703657.0).