Grant's Review Corner: Volume 2

I'm sorry to post this on a Monday and risk taking attention away from today's Monday Mutant, but I felt it was necessary.

Not too long ago, I got the following e-mail:


I’m an incurable puzzler but found that Sudoku was getting too easy.  So I wrote a new puzzle app for iPhone, [name redacted], which is available in the iPhone store for the first time today.  ([link redacted])

The easiest level is kid friendly.  The hardest level (with almost 4 quadrillion, quadrillion, quadrillion possible answers) is “Insane”.  The game is called [name redacted] and, like Sudoku, it challenges us to place a set of numbers in the correct positions on a square grid.  In this case, “correct” means that once placed, the numbers add up to the sums shown for each row, column and diagonal.

A 3 x 3 grid isn’t much of a challenge.  A 6 x 6 grid is incredibly challenging. (Yes, hints are available)

I would love it if you would review the puzzle in your blog.  I would be happy to send you a promo code to download and test it.

I've never considered myself an expert at constructive criticism, but I think I'll make an exception for this app and try my hand at reviewing it. In fact, looking at the iTunes store, I see that you have since released a second puzzle game app, and I will throw in a review of that one as a free bonus! Unfortunately, Mr. Incurable Puzzler, as you might have already surmised from that fact that I have redacted your name and your apps' names, it's not going to be a positive one.

My first criticism of the game is that fact that there is no free demo version of either app. The "try it before you buy it" business model popularized by many shareware computer games of the 90's has proven to be very successful. Why do car dealerships let you test-drive their cars before buying them? Why do grocery stores offer free samples of certain food items? It's to give the potential buyer a better idea of what's being offered for sale. For example, Nikoli has a line of iPhone apps, including Akari Free, a free app containing ten Akari puzzles, and several Akari apps which cost $2.99 and contain fifty puzzles each. Imagine being someone who has never solved an Akari puzzle before. Wouldn't you be reluctant to spend money on this app? You don't know whether Akari puzzles are very interesting. You don't know whether this particular app's interface is pleasant enough to make the puzzles fun to play (because if the puzzles are otherwise well-designed, but the interface is designed poorly, the app as a whole will be very unpleasant to play). The free app gives you a better idea of what you're buying, and whether you'll enjoy it or not. I know that I personally would not have payed for Nikoli's $2.99 apps were it not for the availability of the free apps. My suggestion to fix this: offer a free version of each app with maybe 5 puzzles in each size, and add a version with unlimited puzzles as an in-app purchase.

Before I continue my review, I should probably add that I have not actually downloaded either app, despite having an iPhone on which I could easily do so, and without having downloaded the apps, all I can really judge are their screenshots and their descriptions. While the author has expressed willingness to give me a promo code for one of the apps, I don't have the heart to get his hopes up by asking for said promo code, and then demonstrate my gratitude by posting a negative review. (I do, however, apparently have the heart to post a negative review in the first place. . . .) So without further ado, here are the screenshots! (These screenshots and the puzzles therein are © 2010 "Mr. Incurable Puzzler"; I believe the use of these screenshots for review purposes qualifies as fair use.)
(click to enlarge)
In both puzzles, the objective is to fill each cell with a distinct number from 1 through 9. In the puzzle on the left, the sum of the numbers in each row, column, and one of the diagonals is given; in the puzzle on the right, the sum of the numbers in each 2x2 block is given. Some of the numbers are given in each puzzle.

The puzzle on the left can be solved algebraically, without the need to use the rule that every integer from 1 through 9 appears exactly once. This is because we have a system of seven linear equations with six variables:
a+2+b=11 [i]
c+d+1=13 [ii]
5+e+f=21 [iii]
a+c+5=16 [iv]
2+d+e=15 [v]
b+a+f=14 [vi]
a+d+f=14 [vii]
Note, however, that the sum of the row totals must be the same as the sum of the column totals, which means that any one of the first six equations is redundant, as it is implied by the others. Thus, we really have a system of six equations over six variables, which is still solvable.

Subtract [iv] from [ii] to get:
c+d+1-a-c-5=13-16 ⇒ d-1=a

Similarly, subtracting [iii] from [v] yields this:
2+d+e-5-e-f=15-21 ⇒ d+3=f

Taking equation [vii] and substituting d-1 for a and d+3 for f produces:
d-1+d+d+3=14 ⇒ 3d+2=14 ⇒ d=4

From here, the rest is trivial:
3 2 6
8 4 1
5 9 7
I could have observed that the bottom row must have a permutation of 7 and 9 and figured out which permutation works, but why use logic when mere algebra is sufficient?

In the puzzle on the right, we have only four sums given, resulting in a system of four linear equations over six variables; we have no choice but to use fact that every integer from 1 through 9 appears once. The upper-right corner has 6, 9, and two other numbers that add up to 8 to make up a total of 23, and the only numbers available are 1, 2, 3, 5, 7, and 8; these numbers must be {1, 7} or {3, 5} in some order. The lower-left corner has 4, 6, and two other numbers that add up to 8 to make up a total of 18, so these numbers must also be {1, 7} or {3, 5} in some order. Thus we have 8 possibilities:
- 1 9    - 1 9    - 3 9    - 3 9
3 6 7    5 6 7    1 6 5    7 6 5
4 5 -    4 3 -    4 7 -    4 1 -

- 5 9    - 5 9    - 7 9    - 7 9
1 6 3    7 6 3    3 6 1    5 6 1
4 7 -    4 1 -    4 5 -    4 3 -
The upper-left corner has a sum of 18, and the lower-right corner has a sum of 20, so the remaining two spaces can be filled in:
8 1 9    6 1 9*   8 3 9    2 3 9
3 6 7    5 6 7    1 6 5    7 6 5
4 5 2    4 3 4    4 7 2    4 1 8

6 5 9*   0 5 9*   2 7 9    0 7 9*
1 6 3    7 6 3    3 6 1    5 6 1
4 7 4    4 1 10   4 5 8    4 3 10
The possibilities marked with asterisks can be eliminated because they either repeat a number or use the illegal numbers 0 and 10, leaving us with four solutions.

Wait a minute. Four solutions?


Both apps' descriptions say, "All [app's name] puzzles can be solved with logic so there’s no need to guess. Which is just as well because there are over 300,000 possible answers to the Beginner puzzle and only one is right." Yet one of the screenshots of the latter app shows a 3x3 Beginner puzzle with FOUR SOLUTIONS! How am I, as a logic puzzle connoisseur, supposed to respond to such an atrocity? Actually, let me rephrase that: how am I, as a logic puzzle connoisseur who wishes to keep his blog PG-rated, supposed to respond to such an atrocity? There is no appropriate invective-free response to this kind of horror. You simply do not bill something as a logic puzzle with only one solution, and have it actually have four solutions.

Now let's look at a pair of 6x6 Insane puzzles:
I think it's pretty obvious what's going on here: the program merely randomly permutes the numbers (there are 36! ways to do this), randomly gives you one number per row and per column (there are 6! ways to do this), gives you the sums, and says "Solve it!" "Created by an expert Sudoku player tired of repetitive game boards and short challenges", my eye! Thomas Snyder is an expert Sudoku player, and has the World Sudoku Championship victories to prove it, so I know what kind of puzzle an expert Sudoku player creates. This is more like 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. It reminds me of when I was younger, and I thought I could make a Battleships puzzle by randomly placing the ships, randomly picking some shots, and putting the numbers everywhere. I didn't realize the most important step: make sure there's only one solution.

I see no obvious logical way to start either one of these 6x6 puzzles except to do what I did earlier and list every possible case I find until one of them works. But frankly, after arriving at four solutions earlier, 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. (Edit: According to ralphmerridew, the puzzle on the left has at least three hundred solutions – a far cry from one! – and the one on the right has just one.)

Final verdict: these apps are abominations! You can't review an app on iTunes unless you've actually downloaded it, but were I able to do so, I'd rate them each one star with absolutely no regret. (A one-star rating is especially in order for the first app – it has a five-star rating from someone whose review does nothing to explain the rationale behind the rating except to refer to the app's creator as "padre".) Nikoli's Kakuro puzzles are fun. Nikoli's Sudoku puzzles are fun. These puzzles, in contrast, are not fun, but frustrating beyond measure! Also, remember when I said you should make a free demo version of the app available? I take that back – don't make a free version of this app. If you're lucky, you'll make a buck or two off of people who don't know how terrible the game is because they haven't tried it and don't follow my blog. Make the game good, or at the very minimum passable, and then offer a free demo!

Moral of the story: don't ever ask me to review your iPhone app. Because I just might. . . and mock you mercilessly. In fact, "ask me to link to or review your stuff on my blog" is now officially on my "YOU MAY NOT" list on my sidebar, thanks to these two games.

Update (October 15, 2010): as of now, version 1.1 of the former game, [name redacted], is available. What's new about version 1.1? "Correct an incorrect logo image". That's it. Clearly Mr. Incurable Puzzler hasn't read my review, or doesn't care.

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