I have recently learned a game thru a tutoring training class & am trying to figure out if all permutations are solvable? The game is using number only playing cards (2-9), set out 4 cards, plus 1 answer card. Object is to combine the first 4 cards ( add, subtract, multiply, divide) to equal the 5th answer card. Basically like the 24 game in the forum. My question is are all possible combinations solvable? My gut is yes, but curious how to prove it.
If it can't be proven, could anyone think of a way to write a program to try all the combinations? I thought of writting all the different math function combinations and then just substitute the 4 numbers 1 at a time, but even that seems like I'd be writing a whole lot of unique equations.
I apologize if this is an old idea, but not really sure how to event search for it without even a name of the game.
Thanks in advance.