Support charity, get puzzles!
Patron Puzzles for Philanthropy

Grant's Review Corner: Volume 3

In this edition of Grant's Review Corner, I have chosen not to review a puzzle in a commercial magazine or a commercial iPhone app, but a puzzle that was sent to me in an electronic mail with the subject line "Nice Blog". Judging by the From: field, the sender is from the United Kingdom, and is either a boy or has the surname Boy (and a forename that doesn't look at all like a forename, and is in fact the name of a village in England). Henceforth, the sender will be known as Mah Boy, because he probably just wonders what Ganon's up to. (The puzzle below is © 2011 "Mah Boy"; this review is fair use.)

Hi

This is a fantastic set of puzzles I will be having a lot of fun solving these, though I would drop you a little email with a copy of a Sudoku puzzle that I drempt up (don't think there is one like this) and see what you think?

The same rules apply as normal sudoko but for this use the sums within this puzzle to help you solve it.


+ = 4
+



-


-
+ - - =
=


/
+
-
=
x - =

+
=
=
=
+
+ - =

=




+
-
3 + + / =





=
=
+ - =


I believe that the following review will prove to be of use to all aspiring puzzlesmiths. In other words, it's an absolute must-read.

First things first: I get really tired of seeing people misspell, and hearing people mispronounce, "Sudoku". Look, everyone: it's su, like what a lawyer does, do, like what a lawyer makes, and ku, like. . . um. . . ku. Sudoko, Soduko, Suduku, and any variant other than Sudoku or the dictionary-certified sudoku (lowercase s) will get you Gannon Banned. (Two references to Ganon already? Holy crap.) While we're on the subject of words that people on the internet can't spell, an "atheist" is someone who subscribes to the belief system known as "atheism". "Atheism" is an "-ism", so an "atheist" is an "-ist". An "athiest" is someone who is the most athy. You definitely don't want to call someone athy. And speaking of "definitely". . .

Wait, wasn't there something else I was talking about? Ah, yes, the puzzle. One of the first things this puzzle reminded me of was Arrow Sudoku (1 2 3). Arrow Sudoku has fewer operations than this puzzle (addition, but not subtraction, multiplication and division), and also has fewer run-on sentences and misspellings of "Sudoku" and "dreamt". As such, I can't really assert that this Sudoku variation is terribly original, but at the same time, it's not exactly like something I've seen before, and to be honest, it's not easy coming up with an interesting puzzle with completely original rules.

But here is my first problem with Mah Boy's puzzle: the rules. One thing I've learned from over ten years of experience with the puzzle community is that veterans in said community will pick apart absolutely everything which can be interpreted in more than one possible way. In fact, The Grey Labyrinth even has a game called "Rules Game" where players take turns posting rules that have to follow themselves and all of the previous rules (for example, "All rules must bold every second word."), and a major aspect of the game is debating what precisely a rule means, and whether it's been obeyed or not. (I once tried playing a game of Rules Game with people from outside the GL, and their insistence on going by what a rule was clearly meant to mean and not what it actually means, among other things, ruined the game for me.)

The rules of this puzzle only say to "use the sums within this puzzle to help you solve it." What exactly does that mean? Do the equations have to end up being true? Do they have some other meaning than the obvious, which would allow 3 "plus" 1 to apparently "equal" 2 or 5? Maybe I'm supposed to make them false. Actually, it would have made more sense to use a "does not equal" sign and then force me to make the inequality true, so I'll assume the equations must be true.

Can an equation bend, or be diagonal? Do the equations all read from left to right or top to bottom? I'll assume that they're all straight, and read in normal reading order.

If two cells don't have an operand or equals sign between them, do they make a multi-digit number? Well, that would make the first row [digit]+[digit]=[four-digit number], which is ludicrous. I'll assume that they indicate what's not an equation, then. So something plus something equals 4. That must be 1 and 3 in some order, and to avoid duplicating 3's in the first column, 1 is on the left. Hey, this is easy!

Am I supposed to follow the order of operations (multiplication and division precede addition and subtraction), or operate from left to right or top to bottom? In row 5, we have 3+_+_/_=_. Do I add the first two numbers to the quotient of the next two, or add the first three numbers and then divide by the fourth? As a mathematician, I'm going to assume the first by default unless you specify otherwise. The quotient must be an integer for the equation to be true, and cannot be 1 (or else we'd have a repeated number in the row), so is at least 2. The second number is at least 1, and the result is at most 6, so we must have 3+1+_/_=6. The two remaining blanks can only be 4 and 2. But by the fifth column, something plus 6 must equal something else. Hmm. Maybe we operate from left to right, then.

Let's skip that equation, actually. R2C1 (the cell in row 2 and column 1) is 2, 5, or 6, and from the equation in C1, the cell below it is the sum of that and 1, so it's 3, 6, or 7. But it's not 3 or 7, so 1+5=6. Then R2C3 is 2 or 6, and is the product of the two cells below it, and is therefore 6, the product of 2 and 3, and R2C2 is 2.

1+3=4 _ _ _
+     -   -
5 2+6-_-_=_
=   / + - =
6x_-_=_ _ _
  + = = = +
_+_-_=_ _ _
  =     + -
3+_+_/_=_ _
        = =
_+_-_=_ _ _


My apologies to Mah Boy for switching from his lovely HTML table to this fixed-width ASCII grid, but it's much, much easier for me to copy, paste, and edit.

From R3, 6x_-_=_. The first blank cannot be 2 or greater, because the other numbers can sum at most to 9, so it's 1. The second blank has been established to be 2 or 3 from the equation in C3, and cannot be 3, or else the R3 equation would have two 3's, and is therefore 2. After trivially completing the two equations, we have only a 4 and a 5 left to place in the R3-4C1-3 box, and since there's a 5 in R1C2, they're trivial to place, as well, and R4C4 are R5C2 are trivially calculated. R6C2 is then obviously 4.

1+3=4 _ _ _
+     -   -
5 2+6-_-_=_
=   / + - =
6x1-2=4 _ _
  + = = = +
4+5-3=6 _ _
  =     + -
3+6+_/_=_ _
        = =
2+4-_=_ _ _

R5C3 is 1 or 5. If it's 5, then the equation becomes 14/_=_, which cannot be satisfied with the integers 1 through 6; therefore, R5C3 is 1, and R5C4 and R5C5 are 2 and 5 in some order, making R5C6 4. R6C4 is 1 via calculation. The 4 in R2 must be in R2C5 because of the 4's in the other columns, the 1 must be in R2C6, and the 3 must be in R2C4. By calculation, R1C4 is 5. To complete C4, R5C4 is 2, and to complete R5, R5C5 is 5.

1+3=4 5 _ _
+     -   -
5 2+6-3-4=1
=   / + - =
6x1-2=4 _ _
  + = = = +
4+5-3=6 _ _
  =     + -
3+6+1/2=5 4
        = =
2+4-5=1 _ _

By column 5, 4-_=_+5. Wait a minute. . . 4 minus a positive integer cannot be equal to a positive integer plus 5. Did I make a mistake somewhere, or did Mah Boy make a mistake? Let's look at his solution.

1 + 3 = 4 5 2 6
+



-


-
5 2 + 6 - 3 - 4 = 1
=


/
+
-
=
6 x 1 - 2 = 4 3 5

+
=
=
=
+
4 + 5 - 3 = 6 1 2

=




+
-
3 + 6 + 1 / 2 = 5 4





=
=
2 + 4 - 5 = 1 6 3

4 minus 3 equals 1 plus 5? That's not true at all. I don't understand how such an obvious mathematical error managed to slip by Mah Boy's bright mind. Oh wait I get it. 4 minus 3 equals 1, and 1 plus 5 equals 6. You need to more clearly define what the equations are, and what the order of operations is, or else people will look at your solution and wonder why 4-3=1+5, or 1+3=4526. I personally would draw a loop around each individual equation, much like Zotmeister did with the rummy melds in his recent Heartbreaker puzzle.

See, Mah Boy, this is what happens when your rules aren't precisely clear – people like me will complete misunderstand them, and then get upset because you weren't precise. If the rules had been more precisely defined, then this would have been an easy, but 100% legitimate, logic puzzle. As it stands, though, you should be very thankful that your reviewer was civil, and didn't just say, "After you've scrubbed all of the floors in Hyrule, then we can talk about mercy!" One thing I've learned from over ten years of experience with the puzzle community is that some people can be quite ruthless when it comes to mockery.

6 comments

David Millar said...

This seems like the perfect place for one of my rants about why graphic design is important in the puzzle world, but I just don't feel like typing it out...

zyzzyva said...

Don't forget that the word sum refers exclusively to addition. Perhaps all the other operations should be ignored.

Grant Fikes said...

zyzzyva: http://www.merriam-webster.com/dictionary/sum 5b: "numbers to be added; broadly : a problem in arithmetic"

By that definition of the word, I believe Mah Boy is safe.

zyzzyva said...

Curse your spending more time than I did looking up the word sum.

Anonymous said...

Mah Boy here...

First up your right I'm from a village in England and thanks for taking the time to look over the puzzle. it all made perfect sense to me on how to solve it but now I've looked at it from the solvers point of view and yes it is very misleading so sorry for that. I have also taken on your advice about placing borders round the sums (or should that now be 'numerical equations' )

This is why I wanted someone who knows what they are talking about to have a look, so once again thanks!

Grant Fikes said...

:) Thanks for the kind words, Mah Boy! They make me very glad that I, like a true warrior, strove for peace in the tone of my review, and not something overly harsh. In my previous review, I was a bit meaner, likely because I felt like the programmer of the game was a charlatan, but it seemed clearer to me that you were a newbie looking for guidance and not for money. Even in the case of the other review, though, I edited my post slightly when the creator of the game commented on my post and interacted with other readers, demonstrating commendable sportsmanship and stuff.

Blog Archive