In Which I Review Puzzle Apps #2: It Adds Up

While browsing /r/puzzles, I came across this post detailing that the poster had created an app based off of the Setsquare/Math Square puzzle. Needless to say, I felt the need to review it. Though of course, this genre is extremely trial-and-error based, but sometimes logic can still shine through. Keep that in mind throughout this review.

The first thing that struck me was the choice of graphics. Each of the numbers, boxes, and operations look as if they've been drawn by someone who happened to be lacking a tablet, using Paint XP (not that that's a bad thing if you're solving a puzzle, though), and trying to do so on a train. While I appreciate the amount of effort that must have gone into making the symbols look like such, as well as the randomizer code that randomizes all the symbols to make it look more natural, at the end of the day it's just unnecessary work when you could just as easily use a font from your computer. Not only that, it's visually off-putting due to its irregularity.

Also, if you're trying to make a puzzle with boxes in it, the worst background you could possibly use is a squared background. ESPECIALLY if your boxes are transparent.

A puzzle should have as few detractions as possible from the actual solving process. This is why unthemed puzzle games should, in general, have minimalist graphics; there's nothing else that needs to be shown to the player, so why bother writing code to randomize symbols, or to randomize the colours of cells, when the player is just going to turn off those options if possible anyway?

But enough gripes with the graphics, methinks. Let's actually play the game. So I downloaded it (given that it was free), and started playing. To maximize the possibility of a puzzle with non-unique solutions, I went for a 4x4 puzzle with only addition.

Above is the puzzle that was generated. My gripes with the graphics are far from over, then. For one thing, the sizes of numbers are inconsistent here; note the different sizes of the 21 as compared to everything else.

A second annoyance is the fact that the numbers we should enter are scattered about on top of each other. Take the number underneath the 8. Without looking at any other numbers or dragging the 8 away, what is it? It's impossible to tell, unless you see that 4 isn't present among the other numbers. A better design choice would have been to arrange them in a 4x4 square in an ordered pattern.

The words "flip to check" are upside-down, the timer doesn't work, and neither are any hints displayed, even though the Help section specifically says that we get two hints per 4x4 level.

But in any case, let's get on with the puzzle. From here on, I shall instead use plaintext to represent the puzzle, instead of constantly taking up space with screenshots.

__ __ __ __ | 47
__ __ __ __ | 30
__ __ __ __ | 35
__ __ __ __ | 24
27 45 43 21

Already there are a gigantic number of possibilities and no good way to eliminate enough of them. I could write a script to brute-force the solution if I had the required scripting knowledge, but I don't, so it'll have to be done by hand.

Firstly, we know that 16 cannot appear in the right-hand column, or else the total would be at least 22. Similarly, 1 can't appear in the top row, or else the total would be at most 46.

47 can be formed with [16,15,14,2], [16,15,13,3], [16,15,12,4], [16,15,11,5]... yeah, this doesn't look humanly solvable at all. The only possible way to solve this seems to be brute force. Forget "too hard for the average app user to get into", this is "almost impossible for the average app user to get into". Another couple of words of wisdom originally from Grant Fikes, though modified to fit the situation: 
"This is more likely created by someone who solved five Sudoku puzzles and realized that puzzles make money, so he slapped some programming code together as quickly as possible and called it a puzzle. I see no obvious logical way to start any of these puzzles except to list every possible case I find until one of them works. But frankly, I'd rather play an expert grid in Minesweeper in real life while people are constantly throwing durians at me until I either clear the board and win or trigger a landmine and lose. (And that's just the PG version of what I'd rather do.) If anyone out there is willing to punish themselves by solving these puzzles, or to write a computer program to do so, I will gladly edit this review to reflect how many solutions they have."

But even so, maybe I'm being a bit too unfair on this front. After all, I probably selected the hardest puzzle type of the lot. So I guess I'll try something less impossible.

54 is 6x9, and multiplying either of these by anything would result in a number we don't have, so the bottom right corner must be 1, and the final column must contain 6 and 9. If 9 were in the top right cell, we would have two numbers multiplying to make 11, so that's not allowed. So the right-hand column must be 6-9-1 in that order.

_ * _ - 6 = 2
-   +   *
_ + _ - 9 = 3
-   *   /
_ * _ / 1 = 24
=   =   =
-8  44  54

The bottommost row, because it cannot use 6, must contain 3 and 8 in some order. Clearly neither of these fit with the convention that sums ignore BODMAS in most Math Square puzzles (due to the 44 total for the middle column), so props to the creator on actually being logical there. So these puzzles actually do use BODMAS.

If the middle bottom cell were 3, we could only get a total of at most 26. So the bottom middle cell is an 8, the central cell is a 5, and the top middle cell is a 4.

_ * 4 - 6 = 2
-   +   *
_ + 5 - 9 = 3
-   *   /
3 * 8 / 1 = 24
=   =   =
-8  44  54

All that is left are the 2 and 7. These must be placed in the remaining two cells as 2-7 to satisfy the last constraint, and we are done.

2 * 4 - 6 = 2
-   +   *
7 + 5 - 9 = 3
-   *   /
3 * 8 / 1 = 24
=   =   =
-8  44  54

This was very clearly solvable, so the solvability issues seem only to be with the impossible puzzles.

Now let's try something larger.

In the puzzle to the left, the best place to start is clearly the -347. This is formed by a number of possible combinations, unfortunately, but no matter as there aren't that many to check. The top cell in that column can't be a 1, as there would be three numbers multiplying to make 348, which requires a 29. 349 is prime, so it can't be 2 either. 3 would permit the other three to be 5, 7, and 10. 4 would permit 3, 9, and 13. And so on. The combinations we end up with are [3|5,7,10],[4|3,9,13],[5|2,11,16],[5|4,8,11],[13|2,12,15],[13|3,8,15],[13|3,10,12],[13|4,6,15],[13|4,9,10],[13|5,6,12],[13|5,8,9]. From the third column and first row combined, we can eliminate anything with 13 as the first cell, leaving us with [3|5,7,10],[4|3,9,13],[5|2,11,16],[5|4,8,11] for the second column. The possibilities for R1C3 are therefore 2 or 4, meaning that the rest of the column is either [1, 13, 16],[1,14,15],[2,8,13],[3,5,14],[3,7,10],[5,6,7]. The second row has a little over 200 combinations of R2C2 and R2C3 to check validity for, but because R2C4 has to be >6 to satisfy the C4 constraint, and the product in R2 has to range from 51 to 66, we can remove all candidates from R2C2 and R2C3 greater than 11, as well as 11 itself (or else there would be two 1s in that row). From R2C1 we can eliminate 6, 8, 10, 14, and 16 for not allowing the multiplication to be valid...
I've been continuing on for about 9 hours on this thing on-and-off. BlueStacks, OpenOffice Calc, and Chrome are all eating into my computer's resources, so I'll give up here. If this isn't "deceptively impossible", then it must be VERY, VERY difficult. Probably moreso than the Loop Of Death, since that doesn't require tedious elimination just to get a single piece of the solution.

A couple of final bugs that I notice is that clicking "flip to check" when the puzzle is INcorrectly solved results in the app returning you to the puzzle selection menu. This is very annoying and needs to be fixed. Also, restarting the app and re-selecting "New Game" brings up the tutorial AGAIN. I already know how to play this, thank you very much. Finally, quitting the app loses all your progress.

All in all, the app itself is very solid, but needs i
t's way too impossible for humans to solve, filled with bugs, and has bad graphics. Nevertheless, use of BODMAS over "in reading order hurr durr" has redeemed 1 point for this app.


Verdict: 2/5. Download this if you like feeling extremely frustrated and having to have your phone on for a single 16-hour sitting.

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