The idea of the game seems simple enough. You must make each equation sum balance with the sum at the end of the line. And, the game gives you the current total just next to the target sum for each line. This makes the main game simple enough to beat in one or two attempts for each level. But, by the time you reach the hardcore levels, the occurance of necessary digits has been tightened up enough that luck is no longer an option.

It's at this point that I found it crucial to stop solving the equations on the fly. The windows journal, post-it notes, and calculator had to come up on screen. And, I had to begin serious calculations. Oh, and one other thing had to change. It wasn't until I reached hardcore 2 that I even noticed that everytime you close the game and re-open it, you are given a new set of numbers for the same puzzle. Yeah, I know. That is sick! So, the big change is that you will most likely want to consider not closing the game until you finish a level.

You will still need breaks. Just don't close a puzzle in progress. It's not worth it!

The first thing you need to do is get a screenshot of the whole puzzle to paste onto a Paint program page or something similar, so you can take notes over the top.
The next step is to identify which equations are the shortest and most limiting.

I'm writing this guide after completing Harcore #2. So, I am using my solution to that puzzle as an example. But, every puzzle changes the numbers and only the method matters.

In my puzzle, I had one equation that was to be composed of only two addends. I noticed that there was only one pair of numbers that would equal the target. But, you could turn them two ways: the larger value on top or bottom. It turned out after many failures that this equation was the primary source of all my problems. I incorrectly assumed that the larger value should be placed to fit the intersecting equation with the larger target sum. But, after repeatedly coming up with only one unsolved equation, and the leftover equation repeatedly being only a value of one short, I realized that I needed to switch the order of these two addends within the first equation, since they were only one different in value. This equation was the -23,-24 pair pictured below.

In looking for the next smaller equations, I found 4 that each had only 3 addends, and they were spread around the puzzle. It didn't help that at this point of the game, I was still uncertain from a graphically point of view which direction it was best to solve from. Of course, it is not really the direction, but the size and limiting addends of the equations that matters. So, these four short equations were where the bulk of the calculations had to be completed. But, I did find that since the equation across the top crosses the one shortest fixed equation, then it would be somewhat limited as well. It also has one addend that will be a given because of this. So, I figured that one into the calculations after the four short equations.

Since this section deals with my actual method of calculation, I will share screenshots and images of my method that worked. But, I will also include things that didn't work, in order for you to see the progression in thinking so you can make your own value judgements.

#1 - My first actual attempt to calculate rationally (after many failed on the fly attempts) was the tally method. I simply tallied up first the positive addends, and then the negative addends, and finally the target equation sums, simply out of curiosity about how they fit together. I was looking for rhyme or reason, or some such nonsense. I hadn't a clue what I was doing.


#2 - Still clueless, I tried the careful note-taking method. Yes. I know. I used the post-it notes on screen to keep up with my wandering efforts at rationalization along with the tally sheet above. As I selected addends from the tally page for my smaller equations, I struck them using different colors, and I tried to keep up with the path, to make it easier to go back and take a different path, and ... well it was at least a breadcrumb trail. Like with Hansel and Gretel, those breadcrumbs were for the birds.



#3 - By this point, I realized I was handicapped visually by having my calculations seperate from the actual equations. So, it was here that I opened a paint document and pasted a screenshot of my puzzle to make calculations directly on puzzle. Next to each equation target, I began a list of the possible sets of addends that could be placed within that equation, without considering what the other equations were using at all. This ended up looking like the below screenshot at the very end.

Once I had a working method, I was able to narrow down which addends were causing problems with high demand/low supply. I also had to realize that on the top equation, for example, every single available solution required that a +1 be present in the equation, which meant I could not use a +1 anywhere else. I continued finding the demands of each equation, and striking each option that was deemed impossible, because of this.

Then, I simply solved the remaining equations on the fly until I reached a final one of two equations that looked unsolvable. I made a tally of the sums of the leftover addends; addends which could be interchanged with pairs of addends with equal sums, without changing the value. It looked like this:


When you compare it to my final solution, you see that substitutions made the final equation close up, even though it looked like no match was possible at first.

This game is quite a challenge. Though it can give you a headache, and take a few days to complete a single puzzle, the reward is worth it in the end. I know I am extremely satisfied with the little gold seal at the end of a solution myself. Good luck with your game, and I hope this guide helps you work towards a solution on your own calculations.... without throwing your pc out the window. And, see? I have some energy left after all... enough to recap what happened in this crisis of a level.