I think in a more complete version I'd try to have a better (less rushed) tutorial. Putting a how to play button might be an easy way to cover it too. Could then include details about each unit, costs, strengths and weaknesses etc. That's a nice idea...
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For me it's part of the fun of game dev where you have to think about how things work to make something work.
Some of the problems I've solved in my own games, I've taken the problem back to its basics and worked through the problem in a note or a spreadsheet to catch all the interactions and find an answer. Maybe not the cleanest, but an answer that works.
I completely agree, problem solving in terms of gamedev is always enjoyable. There's sometimes countless solutions, sometimes none, sometimes painfully obvious ones that you don't realise until somebody else points it out to you. There's plenty of creative methods you can use to reach different outcomes. Making a game is almost a game within itself...