Interesting to see how a walkthrough isn't able to solve the puzzle and actually does different things (that don't always work) different times you click on it..
To win lvl 6:
Upgrade Food and Military to lvl 2 and building to lvl 1
Only build the necessary to make Captains and High Priest (and buy the upgrades for them), make 6 captains and 4 High Priests, you will have 130 gold to spare. Throw them as soon as they are all ready at the enemy and you will most likely get the achievement as well, since you heal the captains faster then they can kill you (the enemy didn't have the cannons out before I destroyed him.)
Could use some bugfixes as mentioned earlier (getting all tech points back after reset, I got the achievement about killing 100 men already 3 times, campaign doesn't save properly) but a pretty good game nevertheless.
Not a bad game, it's a bit like the game 24.
Though I don't think all of the combinations are possible. This is very annoying, because there are a lot of ways if it's even possible to get to the number, but when it's not all the time possible, you keep looking but without any succes. I know there is a pass button, but if you look a bit and see it's not possible, then pass, look again and also do the operations, you are most likely too late.
So it could be a fun game, with a little bit more work to it.