Wot I Think: Pythagoria

Pythagoria [Steam page] is an awful lot more like maths homework than it is a regular puzzle game. But if you’re a giant weirdo like me, then you might secretly have rather enjoyed maths homework (the only homework I ever did). In fact, if you’re a colossal weirdo, you might have spent a good proportion of a sabbatical a couple of years ago sitting under a tree in a park with a pad and pen, re-learning algebra from a mobile app. So yes, Pythagoria does rather appeal, despite that. Except, oh dear, my brain. Here’s wot I think:

The puzzles are based around working out the width, length or area of a particular portion of a shape. So you need to know that area is width x height to start with. With just that knowledge, the first bunch of puzzles can be solved. Although, I realised a way in, you’re supposed to solve the puzzles using only whole numbers, no fractions. The “supposed to” part being rather representative of the disappointingly slapdash nature of the presentation.

It looks perfectly pleasant, as if it’s taken a cue from Hexcells, but with no introduction, no proffered tutorial, and only a very crude, scrappy option for making notes on the puzzles, it’s instantly unfriendly. The rule about whole numbers is in fact hidden behind the “?” icon, which rather than offering clues as I’d assumed, instead brings up a rudimentary and poorly written three-step guide, in which this rather key information is buried.

So rather than solving one puzzle by multiplying out “3(15-14/3)”, it seems I was supposed to have approached it from another, apparently “simpler” angle.

Another strange aspect of the presentation is the seemingly deliberate lack of representation of accurate lengths. So two apparently identical widths by necessity are entirely different. Of course that’s a large part to stop solutions being given away visually, but when you’re then solving puzzles based on the knowledge that two rectangles with the same area and same height must have the same width, well it’s jolly confusing on the eye.

It eventually became apparent to my slow, slow brain that approaching these as maths puzzles often isn’t the solution. The main nudge for this is when realising you’re dealing with a width that’s 35/9 or similar – see that and you know there’s likely a solution from another direction.

And then almost immediately, I was stuck. Turns out it was common factors. Awesome, I’ve added that to my repertoire. Except, two puzzles later, completely stuck again. I can see routes to solving them using fractions and a calculator, but that’s not the spirit of the game, so instead I stare in confusion, then ask others for help.

The help comes, and I don’t get it. The explanations come, and I sort of get it. And then I remember how tired I am and how horrible this cold is, and what a miserable couple of weeks I’ve had, and well, yeah, another puzzle I’m not going to quite get appears. Which means: this game is not for me. What it certainly doesn’t mean is: this game is at fault. In fact, if you’ve looked at the screenshots, read this, and thought, “Goodness me, John’s an idiot,” then this is the game for you! I can’t tell you where it goes in the later puzzles (there are 60 in total), as they unlock one at a time. It might just become pictures of kittens. What I need is someone to sit next to me, holding my finger and gently pointing it at all the numbers as they patiently explain it step by step. I’ll smile and nod, and then eventually it’ll be time to go play outside.

So yes, should the maths homework weirdoness be part of your make-up, and in your case be matched by ability, then this is a snap at £1.59.

Pythagoria is out now for Windows via Steam.

39 Comments

  1. Decimae says:

    For a math student who is bad at geometry, the puzzles shown are still quite easy. They are a bit like low-level math olympiad problems(but those are more varied), so if anyone is interested I would recommend looking into those instead, as those are generally free.

    This is not to say you are stupid if you don’t get them, but just that I think that the demographic targeted by this is rather small, as for math enthousiasts it is too easy, and for others probably too hard.

    • jgf1123 says:

      There are two math contests that I know of that use the word “olympiad.” One is MOEMS, Mathematical Olympiads for Elementary and Middle Schools. The other is the IMO, International Mathmatics Olympiad, plus the olympiads that various countries use to select their teams for the IMO. For example, the US uses the USAMO (USA Math Olympiad), the UK uses the BMO (British Math Olympiad), etc. There are similar olympiads for physics, chemistry, biology, computer science, linguistics, etc.

      Among high school students, college students, graduate students, and STEM professionals, “olympiad” refers to one of these international contests where people are selected by their country to compete against the best in the world.

      MOEMS is a contest trying to cash in on the word olympic/olympiad. The problems here are MOEMS material, but not olympiad material. I know this because we get the occasional parent who signs their prealgebra student up for our olympiad training course because the student does MOEMS, which means the student is about 4-8 years of intense study too young for the olympiad course.

      • Decimae says:

        In the Netherlands, there are multiple rounds of the olympiad. The problems posed here are comparable to (some of) the easy problems of the first round, which is just schoolwide. I am unsure of the qualification rounds for other qualifiers for the IMO.

        • jgf1123 says:

          Ah, I see, we have a difference in terminology. Apologies for my outburst.

          In the US, the people who do the olympiad selection process have 5 exams: AMC 10 for 10th grade (2nd year of secondary school); AMC 12 for 12th grade (4th and last year of secondary school); AIME (students who do well enough on AMC 10/12 get invited to take this one); USAJMO and USAMO (students who do well enough in AMC 10/12 + AIME get invited). In the US, only problems at the USA(J)MO or above are called “olympiad”-level, and since only about 500 students per year out of ~350k take these exams, the term “olympiad” is correspondingly prestigious.

          Aside: the USA(J)MO are the first exams in this sequence that require the student to write proofs. I know some countries introduce proofs earlier in their IMO selection process. I think the US doesn’t because there are too many students to do it earlier, but the jump from problems where students find a number to problems where students rigorously prove a result contributes to the reputation of olympiad problems in the US.

          Here is a medium-difficulty problem from the 2015 USAMO: “Let a, b, c, d, e be distinct positive integers such that a^4 + b^4 = c^4 + d^4 = e^5. Show that ac+bd is a composite number.” Under the constraint that the solver can’t use fractions, I would put these puzzles on the AMC 10. Without that constraint, they are more like middle school problems.

  2. Mags says:

    I see what you mean. The puzzle in the second screenshot threw me a bit at first, and solving it can involve common factors, but only as part of simplifying fractions.

    As someone who has previously set maths homework on geometry I can sympathise about the diagrams. If you make lengths look similar it will confuse people, but if you try and put them in proportion than someone will always break out their ruler and try and work it out that way.

    Might give this a whirl. (And I got 9, 7 and 8 for the puzzles in the screenshots).

    • Llewyn says:

      I’m not sure the second puzzle actually requires simplifying fractions. We can deduce that the top row is twice the height of the bottom row because the areas of the two rectangles in the middle column (which must be the same width) are 32 and 16cm2 respectively. Therefore the area of a hypothetical top right rectangle would be 16cm2, half that of the top left rectangle whose width we know to be 14cm.

  3. Todd Hawks says:

    While I like the idea of this, I cannot recommend it.

    First of all it is way too easy if you know what you are doing and probably way too hard if you don’t, second there are still a few “puzzles” that are wrong or ambiguous and third it is way too short. Sure, it’s only $2 but it also took me less than an hour to get through all of it.

    Also the puzzles remind me more of math homework than of a game.

  4. meepmeep says:

    These are called Menseki Meiro, or Area Maze, puzzles, and were invented by Naoki Inaba, a famous japanese creator of logic puzzles.

    It does not appear as though the creator of this game has given him much, if any, credit.

    • Decimae says:

      These kinds of puzzles aren’t particularly creative for math puzzles, and pretty old. They can certainly not be contributed to one author from Japan, which only added the caveat of not being allowed to work with fractions.

      • meepmeep says:

        They are not geometry puzzles, they are deductive reasoning puzzles presented in a geometric form. Hence the fractions ‘caveat’ is not an amendment to an existing form of problem, it is a fundamental element of what these puzzles are. Indeed, they’re barely even ‘math’ puzzles at all.

        • Decimae says:

          Deductive reasoning is math(this kind of deductive reasoning anyway), moreso than the math you got in high school. Math is not just the study of numbers, in contrary, it is the study of deductive reasoning when discussing it in the most fundamental sense. The base assumptions of mathematics say nothing of numbers or geometry(in a direct way), they are just (very useful) constructions.

          These kinds of puzzles (and various others) you find at math olympiads.

          The fractions caveat is just a way to force you to use a certain kind of solution, in a way that annoys me a lot(and is not very well defined). This can be easily proven as if you have fractions, you can easily scale up your problem to remove them(for instance, if one side you wish to use has length 1/2, scale all lengths by 2 and now your side has length 1). Besides, the puzzles here do not require it, so they should be fundamentally different according to you(I still disagree).

    • Mags says:

      Ooh, these are interesting. I might be doing these all night now.

      The stipulation that you can’t use fractions is impossible though. Sooner or later you have to multiply or divide, and, hey! That’s fractions! (Well, division doesn’t actually exist, but if it did, it even shows a fraction in its mathematical symbol ÷!)

  5. Aleister Crowley says:

    How curious… I wonder why several paragraphs of your original article was hastily and furiously edited in the last five minutes? Possibly because of your blatant slander of that Steam user who had a differing opinion than you? Sure, he may indeed clearly be a fool, no argument there, but what does that make you for unprofessionally using your RPS article to mock him? Not classy. I was going to reply to the original comment who pointed this out, but naturally, you deleted that as well to cover your tracks. Sorry John, it’s too late; we have the screenshots. If this isn’t evidence that journalism and good writing isn’t your forté, then I don’t know what is. Please Rossignol, sack this cringeworthy hack before he really puts his foot in his mouth.

    • Premium User Badge

      particlese says:

      Seriously? You do know the article could still easily be altered client-side to be about cheese and hobos or something, right? If you want yourself some doritogate, have at it!

      Regardless, sounds to me like he has made appropriate use of the elusive Edit Button. I (royal-we?) might vote for a slap on the wrist if it were offered and the heinous crime admitted to, but then I’d get back to enjoying his writing. Please keep your sack to yourself.

      • Xocrates says:

        As the author of the “original comment who pointed this out”, I fully agree – and expected – that the offending section be removed.

        That said, while I’m not hugely bothered by this, I would have preferred he kept my original comment with some sort of admission of error attached as opposed to simply trying to erase any proof of wrong-doing.

        John made a mistake, that’s normal and forgivable, particularly since I’m aware he’s been through some bad times.

        But he could have handled it a bit more better.

        • Premium User Badge

          particlese says:

          Ah! Yeah, I agree with you two on the deleted post thing; I forgot that point. That’s pretty tacky unless your post was strongly uncivil — something I doubt, given your posts right here.

          I was also thinking it probably stems at least in part from the hard times, but I decided that involved too many feels to be a useful argument against the above seemingly serious hyperbole. :)

          • Xocrates says:

            Just for the sake of openness, my original post was more or less:

            “Wait… wait waitwaitwait…

            Did you honestly use this review to name and shame a random steam user you just happen to disagree with?

            wow!”

            A bit blunt perhaps, since I was caught completely off-guard, but I don’t think it was uncivil.

    • Premium User Badge

      Grizzly says:

      I know that John is occasionally blunt, but I do feel that his detractors take his behaviour a lot worse then it actually is.

      • Xocrates says:

        In this particular case it was actually pretty bad, to the point I’m incredibly happy that the offending section was quickly removed AND that the RPS community is as mild as it is.

        I honestly do hope this never happens again.

        • Premium User Badge

          Grizzly says:

          I was more referring to the OP being in line with a general trend, not with your original complaint :-)

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          John Walker says:

          I cut and pasted a publicly available review of this game, freely posted for all to see on Steam, that was astonishingly vitriolic. I thought it was interesting for a couple of reasons. 1) It highlighted just how differently two people could receive the same game – me finding it impossibly difficult, he finding it insultingly easy. 2) It highlighted, I thought rather immodestly, how traditional balanced expert games reviews still have a useful place on an internet of 0/10 or 10/10 user extremes.

          My colleague Graham disagreed, and made the decision to cut it, and since I employ him to be far smarter than me about this stuff, I always accept his wisdom.

          And yes, lord knows the hate some people have for me must take far more energy than I could possibly deserve.

          • Xocrates says:

            Then I’m sorry to say you failed on both points. It came across as nothing more than you mocking a random Steam user for disagreeing with you.

            Were this site community larger and less polite, and the dude could probably expect to be on the receiving end of a lot of hate.

            You could, at the very least, quote the review without naming and linking to the author directly.

    • disconnect says:

      W E H A V E T H E S C R E E N S H O T S

    • Premium User Badge

      John Walker says:

      Oh noes, not the screenshots?! What will I ever do???

      I didn’t “slander” anyone! I quoted his review, and said it was another point of view, in order to mock how astonishingly vitriolic it was.

      It was decided by our managing editor, soon after publication and while I was shopping in Sainsbury’s, that it added nothing useful to the review, so he deleted it. I assume he then deleted a comment referring to it as it was no longer relevant.

      Next time Jim and I have a meeting of co-owners of the site, I’ll be sure to suggest he fire me.

  6. FLoJ says:

    link to static.guim.co.uk

    There was a fun one published in the Guardian a few months ago :)

    full article: link to theguardian.com

    and solutions: link to theguardian.com

  7. Premium User Badge

    particlese says:

    Oh, jeez, that disproportionality sounds like it would drive me up the wall. The anti-cheat reasoning for it is clear, but I’m not sure I could appreciate the resulting absurdity of it. Maybe it would work if puzzles were instead somehow posed as a network of disembodied numbers. Then it would prevent geometry-based guessing while avoiding the current solution’s confusion, chaos, implosion of reality, rioting in the streets of the resulting surreality, and so forth.

    Might give it a go anyway, though. It looks like it’s otherwise pretty logic driven, and that might be enough to distract me from disaster.

    • Josh W says:

      They could also fix this if they represented the puzzles as pencil sketches or something; a sense of inaccuracy in the presentation, similar to if I was drawing it out on a piece of paper myself, would make it easier to focus on the numbers.

      Otherwise, it reminds me of busy architects who alter the measurements on drawings without altering the drawing themselves, resulting in accidentally impossible non-physical spaces.

  8. 49152 says:

    Maths puzzles you say? Less than a minute later this was bought and installed.

    There may be something wrong with me.

    Odd for someone to describe an individual as the creator of what are stock maths homework questions though.

  9. Llewyn says:

    I doubt this is for me. My last academic maths experience was sitting STEP some 20-odd years ago (do they even still have that?) which was not a fulfilling or successful experience.

    Still, £1.59, it would be hard for it not to be worth that.

  10. bill says:

    Which app did you use to re-learn algebra? Cos I’m trying to do that right now after I realised I’d forgotten everything I learned about maths in school.
    Currently using link to mathsisfun.com but something mobile would be handy.

    As for this game, only looking at the screenshots here and on steam, it seems to be more of a logic puzzle than a maths puzzle, right? Unless I’m totally mis-understanding the concept.
    It’s more like Sudoku in that it’s about finding the right steps to the solution, rather than about actually doing any maths. (The answer to the 1.9 screenshot can be guessed in 1 second using nothing more than basic addition, right?)

    That said, I have no idea how to do the 2.5 and 3.2 ones in the steam screenshots… but I guess it’d introduce the concepts for those as it goes.

    So it seems the main flaw is that the game doesn’t introduce itself very well.

    • bill says:

      ooh ooh ooh. Quick refresher on pythagoras theorem and actually (I think!) 3.2 is pretty easy. But it needed me to break out my mental times tables… which are very rusty.
      6 right?

      Still can’t do 2.5

      • FLoJ says:

        For 2.5:
        – Work out the horizontal of the 12cm2 box
        – Work out the vertical size of the 5cm2 box
        – Work out the horizontal of the 18cm2 box

        I get it as 6cm :)

        • jgf1123 says:

          That approaches uses fractions. Here’s how I did it without fractions:
          – What is the width of the 12 cm^2 box?
          – What is the width of the 5 cm^2 box?
          – Now draw the missing rectangle above the 5 cm^2 box. What is its area? What is the combined area of this rectangle and the 5 cm^2 box?
          – Compare that area to the 18 cm^2 box. What must the ratio of their widths be? Since we know the width of the 5 cm^2 box, we know the width of the 18 cm^2 box.
          – Now add 2 cm.

      • jgf1123 says:

        The answer to 3.2 is 6 cm^2, yes.

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      John Walker says:

      I used this one

      link to play.google.com

      and this one

      link to play.google.com

      They were far from perfect, and even had some incorrect examples in there, but did the trick.

  11. Hakusho says:

    I think i need to buy this.
    I did not really like Maths homework…. but it has Steam Achievements!

  12. jgf1123 says:

    Bought it, finished it in an hour under the no fractions rule, wrote an overall positive review on Steam. Summary: don’t expect to learn geometry, but you may become a better puzzle and problem solver by playing it. It’s worth the $2, though it can be repetitive and/or trivial at times.

  13. horsemedic says:

    The rule about whole numbers is in fact hidden behind the “?” icon, which rather than offering clues as I’d assumed, instead brings up a rudimentary and poorly written three-step guide, in which this rather key information is buried.

    What mid ’90s-manufactured time machine did you tumble out of into the office of a games reviewer if you assume a “?” icon indicates a clue before a help guide (in which the key information is “buried” under three short sentences.)

    I expect opinions in review, but not misleading language to support them.

    • Josh W says:

      Focusing on hints and carefully paced puzzles is in some ways a more natural way to teach a game; you make the interactions so simple at first that people just learn the interface, and work up from there.