Most quests I've been through that worked like that, you don't even need to complete the construction. You sure you didn't just miss seeing the check after having started the first construction? It does go away after a few seconds.
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I would click on the quest and the progress bar would still be red, indicating the quest had not been fulfilled. :/ But both this comment and ByeOrDie's clarify where I went wrong...
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The build quests only require you to place the building in your city. Not have it finished constructing during the quest, so if you place the building in your city before you accepted the quest, then that won't count towards it.
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I think this must have been what I did. I can no longer recall if I started constructing the building before the quest came along (in the hopes of getting it done sooner, since I figured it was COMPLETION of the building that counted, not just STARTING construction), but I made that mistake just tonight when I started construction of a military building while doing some earlier quests. When the building quest came up, the structure still had about five hours to go, but I had the sneaking suspicion that just placing the building in my city should count toward the quest...so I sold the in-progress building (at a loss, sigh) and started another one now that the quest was in progress. And what do you know, there was the green checkmark immediately.
Didn't have to wait 10+ hours for it to build...
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I guess I took the practice of starting the 24-hour productions earlier and applied that to the construction of buildings as well, when the results are not the same.
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Thank you both for clearing that up! Had to learn the hard way, twice. Good thing I have loads of supplies and coins to burn. ;_;