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Ten seconds of math (mental-math-trainer.com)
248 points by countryqt30 on Nov 26, 2014 | hide | past | web | favorite | 117 comments

Noticed some fun SEO hacking at the bottom of the page:

<p class="hardly-visible">puzzles calculate formula mathematics maths decimal number calculating mathematician multiply measurement probability equation division measure homework units word problem solve converting resources tessellation anxiety math problem problems convert unit ratio number trigonometry perimeter divide mental multiplication calculus math quadratic triangle teselation problems pi change equations homeschool fraction tesellation converter maths problems fractions conversion math prime mathmagic Theorem calculator percent magic homework fractol volume math math tesselation math math math mathematical statistic unit geometry math polygon square math pre-algebra algebra word statistics games area math Pythagorean fractal history trapezoid maths conversion circle numbers circle </p>

They should remove that. It'll get them smacked by the google spam team eventually.

Wow it's early 2000's style of SEO - lots of individual words rather than actual searched-for phrases.

Could Google theoretically calculate the probability that some text on a webpage is extremely hard or impossible for humans to readily see based on info from the source page about the background and text?

Not just theoretically. Very concretely.

Well I said probability because depending on how complex the background is such as photographs, video, or some weird scrolling behavior, there could be some hindrances to having a computer accurately or computationally-efficiently determine this.

Google uses filters, which run in different intervals apart from the main algorithm and have different effects for a page or the whole website. This is why spammy SEO tactics often "work for a while" - until said computationally intensive filter catches them and often punishes the whole website. Prominent examples for these filters are Panda [0] and Penguin [1].

[0]: https://en.wikipedia.org/wiki/Google_Panda

[1]: https://en.wikipedia.org/wiki/Google_Penguin

If not already... You really shouldn't do stuff like that. SEO 101.

Yeah, and I don't understand why people still do that. It may work. For like a couple of weeks, before you get banned forever.

It's even easier to do stuff the right way, especially in a one page design. Just leave the logic up above. Then put a long, well written text about math, the importance of brain exercise and a description of the game with well divided H1/H2 headings, below it. Here's all the SEO you need. The link from HN and all the sites that scrape it will do the rest.

https://github.com/michaeljakob/10-seconds-math you can submit a PR to remove it

This SEO spam is not in the Github repository. It seems Michael Jakob knows full well that it is frowned upon.

When I was near the end, I pressed backspace to clear my answer, and it wound up navigating me back to HN, wiping out my results.

(I hate backspace-to-go-back. It's the worst feature in a browser. Is there a way to turn it off?)

This mental math exercise is a cool and fun concept! Good execution.

> I hate backspace-to-go-back. It's the worst feature in a browser. Is there a way to turn it off?

I love this feature. Makes browser navigation keyboard friendly.

Different strokes for different folks I guess.

What about [alt]+arrow?

I really like Cmd+[ and Cmd+] for back/forward. Also because Cmd+Shift+[ and Cmd+Shift+] are tab prev/tab next.

It's also "the worst" feature in Windows Explorer folder view; when it switched from going up the folder tree to going to the previous folder and throwing an error if that folder doesn't exist anymore.

In Chrome I think you can only do this with an extension. I use BackStop.

I love backspace = back button. What I need is delete = forward, so I can undo the action when I accidentally trigger it.

I thought that maybe the ranking was real.. no its not

  function getRank(score) {
    // TODO we should add a real ranking one day
    return Math.floor(100 * Math.min(Math.E * score / (ONE_BARELY_REACHES_THIS_SCORE * Math.PI), 1));

WTH?? then why release it in the first place.. That's the only crucial step in this whole concept..

It can't be the crucial step since one could open javascript console and type

  foo=true;$("#question-answer").bind('keydown', function(){if(foo)$("#question-answer").val(eval($("#question").html()));$("#question-answer").keyup();foo=!foo;});

okay.. now so.. what is the crucial step in this whole thing?

is it generating random numbers with random operators i between them and evaluating whether the solution given by the user is correct and count the number of correct responses??

By crucial step i meant the logic on how he calculates the percentage of people below.. how it changes when the operators used are changed.(is it dependent on operators in the first place? ) and when the range is changed? etc..

Indeed somehow I managed to do better than 100% of people with a score of 432; I thought it was a reasonably good result but hardly worthy of 100%.

Damn, and I was so proud of my best score.

After going for several minutes I gave up.

In addition to a leader board, it needs to: - Have a time limit and see who can get the most calculations done on that fixed time - or, have a fixed number of calculations and see how fast people can answer them - or, it could get faster as you progress

The calculation of the "you are better than X%" needs to be fixed because everybody in my office was better than 100%

I was thinking maybe instead of a leaderboard, graphs/analysis of raw data would be very cool, such as accuracy and answers per second and total score, and how those stats match up with the rest of the people who have played

For me there is a set of calculations I can do without thinking and there is a set where it takes several seconds to figure the solution out. No smooth transition. Is it the same for you? If yes, this would make tuning this game pretty hard because it is either to easy or to hard.

Yeah, I was sent a link to a similar site yesterday (timed mental arithmetic/algebra), and was thinking exactly the same thing: divided by types, half the problems I could do instantly with almost no thought, but the other half, regardless of how easy, took a few seconds.

I noticed that with, for example, multiplication, I have a set of rote-learned answers for calculations that aren't 2, 5 or *10, and if the answer isn't one of those answers, I'll get the closest answer I can remember, and work back/forward from that. It's entirely habit, and I can't stop myself doing it. Algebra as well, I always have a moment where I swap parts of the equation in my head; even if it's utterly simple, there's still a noticeable cognitive step.

When I turned squares on I hit a wall at 23^2 etc. I can do it, but it's 10 seconds just to do that calc. Basically anything bigger than 14.

For the rest it was more about staring at the numpad (which I never use) and typing in my answer. If I typo'd I lost several seconds as I'd not have a finger on backspace :(

Squares are actually pretty easy with a mental math trick.

n^x = (n-m)(n+m) + m^2

so for 23:

23^2 = 20*26 + 9 = 529

Nice! I made something similar a while ago - http://www.speedsums.com :)

I like how it remembers your worst answer and reminds you what's the correct answer! The victory animation was a bit terrifying though, like one of those "stare at the screen" pranks :) Cheers

I instantly remembered speedsums once opening this site there. Went to the comments to check to see if it was referenced. Boom.

I crazy love how it auto submits your answers for you, super convenient! My dad made me do similar online mental math exercises when I was younger and I always hated how clicking "next" reduced my time. Does it take into account what your settings were when it reports your score relative to others?

Doesn't pressing Enter generally work? I'm usually surprised by how many people click a button to submit a form.

This was a long time ago, I'm sure if Enter had worked I would have used it. They could have been using poorly implemented AJAX.

I got redirected to the Google Play store. If I'm on Android why can't I use the website like everyone else? Please don't assume I want to install an app.

I also got redirected... I'm on Windows Phone.

People should start differentiating between mathematics and arithmetic.

Arithmetic is a (small but fundamental) subset of mathematics. I don't see anything wrong with the title.

Arithmetic != Mathematics

just as

Typing != Programming

Sure, typing is a useful skill, it's part of programming, but is it programming? - no of course not. In fact it's insulting to programmers to make the confusion.

It's the same with those of us who have taken the time to get good at mathematics - it's not arithmetic. Being good at arithmetic does not mean you are good at math, being good at math does not make you good at arithmetic.

This confusion is especially detrimental to children, many of whom will be put of mathematics because they equate it with the wrote learning and peculiar mental gymnastics of arithmetic, rather than what it is: An exploration of the beautiful and fundamental symmetries that emerge from structure and process.

Yes, but arithmetics is a branch of maths, whereas typing is not a branch of programming.

Maybe they plan to extend the site to include trig, algebra, calculus, etc. problems?

Not really. Mental arithmetic is the ability to move numbers around in your head, it really is equivalent to being able to type as a programmer. Mental arithmetic is to number theory as being able to type is to programming. That you do not understand this, shows that you too have been damaged by the standard teaching of maths within education - pre university level.

> Not really.

Yes, really. "Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation" -- http://mathworld.wolfram.com/Arithmetic.html

> Mental arithmetic is to number theory as being able to type is to programming.

To paraphrase you, number theory != mathematics. (But number theory ⊂ mathematics, just as arithmetic ⊂ mathematics.)

> That you do not understand this, shows that you too have been damaged by the standard teaching of maths within education - pre university level.

That's a bit rude, and also inaccurate.

I think this is one of the many cases where you emerge out the top of an ideath to come right back to where you started at the bottom, but for different reasons.

I grade school many are taught that math === arithmetic. Then they get to interesting stuff in high school and college and realize arithmetic was just a tiny part of the story. So many at that phase are emphatic about refuting what they were told early on about arithmetic being math. Then when you calm down from that notion, you can get back to realizing that while arithmetic is only a small part of math, it is still very much a part.

Mental arithmetic is to number theory as being able to type is to programming.

In other words, it's something basic that you have to be able to do efficiently in order to achieve higher goals.

On Debian (and, I'm sure other distributions of GNU/Linux) the 'bsdgames' package contains a simple program called 'arithmetic' which poses similar challenges, albeit reduced to the most elementary operations: addition and substraction. Call as

    arithmetic  -o '+-x/'
in order to add multiplication and division.

I find it a handy supplement to 'gtypist' in order to train touch-typing of numbers.

On a side-note: I'm surprised at how scarce such software is - pitiful as it may be. But then, the advancement of the human intellect isn't at the forefront of our cultural conscious, is it?

This feels like a lot more than 10 seconds. You tricked me.

Just for anyone who feels pleased with their mental maths and thinks they might be able to take on their calculator head-to-head:


your paste lost an asterisk * in the first replace statement

It's boring at some point. You should make a countdown instead: you have, say, 1 minute to answer as much questions as you can (with an possible skip button).

At first I actually thought that's what the game would be. I was pleasantly surprised that it was more like juggling, by the end when I had 1-2 seconds per problem, I was far more interested. Something about keeping up the "combo" but testing my arithmetic was quite pleasurable.

It'd be pretty cool if this actually had leaderboards, perhaps one leaderboard per set of options, limited to clusters so as to minimize the amount of leaderboards. Such as "arithmetic, multiplication+division, arithmetic and mutliplication+division, free for all" Was pretty upset to see that the result for scoring 5xx was the same as my next run of 7920

A leaderboard wouldn't be meaningful -- Client-side code isn't secure, and people could set scores to whatever they like. Or, just for fun, I played with the page a bit via dev tools, added in a script to automatically calculate the answer, put it in the input, and trigger the keyup event to run their submit function... worked great.

There is nothing wrong with client-side tools. I have a few on my site that get decent usage. But unless you put some security and validation on the server-side, any data coming back is not trustworthy.

For me there are certain mental calculations that take longer to process than others. 2 + 2 is super easy. 7+8 is not as immediate. I need a program like this that learns which calculation take me longer, even if it's just slightly longer, and then drills and drills my weak points over and over again. That would be a real mental math trainer.

With a bit of tweaking, Anki [0] or another Spaced Repetition Software program will do just that. You can configure it to categorize your answers by how fast you answered them. Then it will make the easy ones less frequent.

I used it to memorize the times table up to 20x20.

[0] http://ankisrs.net

Is that stack available for times-tables ready to install and use, if not can you share it? Thanks.

I just generated a text file with a quick shell script and imported the output into Anki. I have neither anymore, but the text file just looked like


This just showed me the need for a numeric keypad. Half of the time I spent was looking for the right keys or correcting mistypes - normally I think I'm pretty good getting $ and * every time without looking.

I think the change in performance here has something to do with never returning to the home row; I'm just completely lost on laptops.

Does it speed up or end eventually? I stored up 150 seconds left before I decided to quit (score of 2529).

For a moment I had the idea it was speeding up, but later on I felt like it was just an illusion. Got to 5661 before stopping.

yeah... it never ends if you're too fast.. lame...

Pretty cool, zombie mode morning with addition only and number limit of 30: "You scored 504. You are better than 100 %"

I am sure this will be easily beat by all the caffeinated people pretty soon.

Updated: this is actually easier with all the other options enabled because you get easy things like sqrt([4, 16, 25]), x * [0,1], and x / [1, 2] a lot. I was actually over 30 seconds on timer when I hit 18^2 question. "You scored 576. You are better than 100 %"

Updated 2: I tried raising number limit to max (1000) and suddenly life on hard mode. I got through 272/16 and 930/31, but third question 127 * 49 killed me. "You scored 64. You are better than 27 %"

333 was also better than 100% for the same settings...


No real ranking data is being used in this calculation

What I meant to way was that you're not being ranked amongst your peers. Saying that you're "better than 100%" or any other percentage is just a result of the assumption that a really good score is 200.

if (sliderMax > 100) { sliderMax = 100; } score = Math.ceil(numAnswersCorrect * (sliderMax / 10 + numOperatorsEnabled))

Score multiplier and number of operators selected directly influence the score. So setting slider to 10 and enabling all operators gives 7 points per question and increasing slider to a 100 raises that to 16 points per question.

I've played with many of these. And this one is pretty good. One thing that I'd like to see is a "verbal" option in these types of apps. I have trouble "hearing" math and keeping it in my head. I envision an app speaking the problem, then you have to type in the answer. It requires both math and keeping the problem in your head. Lastly, a verbal or speaking option maps to many real world scenarios.

>I have trouble "hearing" math and keeping it in my head.

I have the exact same problem. Interestingly, it's a problem for me both in my native language and in several other languages I learned to fluency. So clearly, the "hears numbers" part of my brain is deficient.

I've actually practiced to try to overcome this, and made no progress.

On the other hand, I'm quite good at visual calculations, and also at remembering numbers when I see them. So if I bother writing down a phone number, I can easily remember it for a long time.

But hearing it? Nothing.

http://ccccnews.herokuapp.com/ Use the numpad.

If you don't care about the setting: 1. Click "Play game" 2. Press 2, Enter, Star once it loads.

Make 24. Enter the two intermediate results. Numpad plus repeats the question.

I don't know if this is a good place to start if you have trouble hearing but might be fun for practice anyway.

I actually made a mental math game for Android not long ago. The concept is different though - it's about choosing the operations to reach a target number. I would appreciate any feedback!


I have this on my phone, my 5 and 9 year olds like it!

I find the hard level pretty hard - it would be good IMO if you could change the mode to include negatives (maybe roots and squares [+other powers?], like here) and to expand the number range to. I seem to remember someone mentioning (probably on here) that they played a mental maths game where you had to give an operation on a number, you didn't say the answer but the next person had to add an operation, there was always a range (age adjusted) that the answer had to fit within: was that game the inspiration or was it just a novel idea for you?

Like the game anyway, thanks.

Thanks for the feedback! If the hard level is pretty hard, wouldn't adding more operations make it even harder? I kept the number range small because I felt it would be too hard to do mentally otherwise, but I'm definitely open to extending it. The idea was novel for me but I was quite certain it has been done before in one way or another.

It would probably make the hard level even harder (assuming unique solutions then definitely) but for the lower levels it would provide a wide range of play styles and so more replayability - I'd probably be more inclined to play intermediate with wider ranges and/or other operations than to play hard in "simple" mode.

In my opinion giving that much freedom (all those settings) to user is not good and ruins the gameplay. I'd prefer such game to start simple and increase difficulty by itself. I find this one almost perfect: http://games.usvsth3m.com/maths/ although it lacks more levels.

Champion of addition

setInterval(function() {document.getElementById('question-answer').value = Number(document.getElementById('question').innerHTML.split(' ')[0]) + Number(document.getElementById('question').innerHTML.split(' ')[2]); $('#question-answer').trigger(jQuery.Event( 'keyup', 16 ));},500)

As a farmer, I am deeply offended by this game.

Was not disappointed. Was half expecting a 3 page long article about some epiphany over 10 seconds of math contemplation.

I like this. Duolingo does something similar for language practice. After you've completed lessons you can do a timed practice session where it will ask you to translate words you've already learnt. It counts down and the quicker you get it correct the more time gets added to your countdown.

New features! - difficulty increases over time - motivations on correct answers - slightly adjusted question difficulty - sliders are disabled while scoring :)

Feel free to test it and let me know :D http://www.mental-math-trainer.com/

Something similar on android: https://play.google.com/store/apps/details?id=mental.care.ac... I haven't updated it a while, but feel free to try it

Too bad it's things like this that make average people think math is little more than arithmetic.

I'll quote one of my math professors: "At this level, nobody knows how to subtract!"

Scored 47232 before giving up...

For those who are still struggling with mental arithmetic, or kids just learning, this seems like it would be a great way to practice --- there is a a certain addictive quality to it, like "flappy bird".

Where can one learn about techniques for getting faster at mental arithmetic?

OT: I ended up being mostly fascinated with the FB and Twitter share buttons

Why? I can't see anything interesting about them, they seem stock?

Play the game, and then let it fail so you lose, then look at the FB and Twitter share buttons under your score :-)

The number limit should be more granular, or even it would be nice to be able to "pin" one number... i'm thinking of studying times tables for my children! other than that, very nice

Agreed, great tool, would love to be able to set for my kids to focus on certain times tables. Really cool.

Good game, it has that silly 'flappy bird' style appeal that it is difficult to keep going - they should reduce the additional time given per question to go more in that direction.

Suck at arithmentic. But this took me 20 seconds to write.

setInterval(function(){ $("#question-answer").val(eval($("#question").text())).trigger("keyup") }, 2001);

This is pretty cool but, is it a game? I can't see how solving math problems under a time limit can be useful for anything besides a math exam or some other academic test.

My experience has been that mental math training, while not directly useful, generally seems to improve the way my brain works and enhances my analytic thinking.

This effect is a lot more tangible with longer, multi-step problems. In college (physics major) I made a point of doing every integral in my head if I could, and over time I found that my mental 'scratch space' seemed to be getting longer - that I could hold more in my short-term memory at once.

I've also observed that being a person who is 'good at math' approximately correlates with being a person who does math in your head.

[Related observation: that students strongly segregate into "good at math" vs not, as though many people are completely incapable of a mode of thought that comes naturally to others. I think it's trainable, and people who never do any math, especially in their heads, are specifically not training it.]

These are entirely anecdotal and I'd love to find more concrete data, but, right now I would absolutely vouch for mental math training.

General problem solving and critical thinking is good mental training. Timed arithmetic drills are neither, and I really should hope that arithmetic doesn't count as "critical thinking" for the majority of the audience on HN.

I have to agree - for all the talk of "mental training", is there any actual evidence that arithmetic drills will actually help with problem-solving and critical-thinking?

My point in the parent post was that I have a lot of anecdotal reason to believe this. Enough to be pretty confident I could find actual evidence, but I haven't looked very hard.

No one has claimed that arithmetic trains you at critical thinking. It trains you at a certain kind of abstract thought, and I'm specifically stating that I have found that very valuable.

This is just a slightly-gamified version of mental arithmetic training flashcards. Are you questioning why mental arithmetic is useful? There are lots of places where it can improve your ability to understand the information around you.

If you're reading a graph, you should be asking yourself a ton of questions about it. A lot of those questions can be answered with mental math if you're proficient at it. If you weren't, you'd have to resort to a calculator or other tool, and the switching cost keeps most people from doing this:

examples: what's the ratio between these two values? How did it change? I have this per minute (or, in my case, a per 4 minutes) rate. What is that per day? How much did that drop by (absolute and relative)

The point isn't that people who are bad at math can't compute these things in the real world. They can, and often do, whether with calculator, on paper, slower in their brains, or with a different query or better analysis tool. But people who do these operations quickly mentally do it more, do it more quickly, and can digest and filter more numeric information.

A long time ago, I read an article concerning mathematical problems and how solving them improves (probably short term) intelligence. It turned out that simple arithmetic was the most useful. Of course, I can't find the source right now.

And here's a reverse-math extension. (and No funny SEO) :)

I think clicking is easier than typing.


A mate of mine is behind - http://numbertap.com/

Similar concept but with cross platform multiplayer.

My score: 4785 :) (all options, number limit = 50)

I wonder if there would be any difference in the results if the numbers were stacked vertically instead of horizontally

Minor bug I noticed: When the timer hit zero it went back up to 1 second and then down to 0.

FF 33.1 on Mac if that matters.

Square roots should be improved, just ranges from squares of 0 to 6.

With default settings:

You scored 666 You are better than 100 %

At default settings, only boredom makes me run out of time. [Actually, waiting a full minute or so for time to run out was too boring, too. I changed settings before that]

Addition up to 1000 is reasonably fun, but also feels like it would be doable for a really long time with a physical keyboard and at full attention (I got 3328).

That also is a weak point of games like this. IMO, games are good if you can play them without attending to them or when they provide interesting problems. Games with dull problems that require your attention fail. A prime example of the first game type is Tetris; I use to say that your spinal cord can play it. Examples of the second type are Sokoban and (a million times so) DROD (http://en.m.wikipedia.org/wiki/Deadly_Rooms_of_Death)

With all operations checked and numbers up to 1000, I find I need more time, and scoring seems brutal (only 16 points after 2 or 3 correct amswers?)

I also find it a bug that you get subtractions with negative numbers as answers.

Finally, is it a bug or a feature that starting a game gets you the same problem and partial answer that the last game finished with? It helps in doing a post-mortem, but can make it really hard to get that first answer right.

I got lower than you after you left this comment with default settings (only addition) and it also reported better than 100%.

"You scored: 315. You are better than 100%". Why do I think their countdown timer needs some work on MobileSafari? :)

got bored at 855 and let it run out, and it would seem I've bested 100% of you

Got same result 16 min later, needs floating points :)

352 with all options and limit 1000. Anyone do better? :)

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