Just played your game.
Liked the idea, as some people have said, it could do with some balancing. It wasn't clear to me that spawning NPC's reduced your population, or the cost of a particular unit, but a fun game for a phone.
When I played, I didn't notice the population until near the end of my play, are you planning on adding in instructions on a main menu? A how to play might help as I found myself so focussed on the enemies coming in that I wasn't looking at the bottom of the screen. Could just be me though, been a long day.
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...