Halfsies

brilliant.org

494 pointshysan145 comments

100%! Not sure what this measures, but I've spent decades trying to gauge whether a design is one pixel off, or if some minor change has affected the layout of something. Maybe that was all preparation for slicing America in two using an Australia-shaped knife.

Congratulations, you may have discovered your unique talent! Now, about the monetization strategy ...

100% too, but I was shooting blind for the last few. Not sure if I just got super lucky or if the brain is better tired think at setting that.

I guess “Australia-shaped cookie cutter” would be more accurate

I wonder, is a cookie cutter a kind of bent knife - or is a knife a kind of straightened cookie cutter?

"Maybe that was all preparation for slicing America in two using an Australia-shaped knife" one of those sentences I feel like no one has ever said before (/r/brandnewsentence material)

I don't think HN is the place for r/subreddithashtags

now if only the America vs Australia cut was on spherical (or ellipsoidal I guess) geometry rather than projecting both countries to a plane prior to slicing

I got 97% on the first part and was impressed with myself, but you're experience with design work is certainly the professional difference. That's impressive!

97% here too, with 6 out of 8 perfect cuts. Much better than I expected!

95pct, 4 perfect splits, did better than I thought I would

Congratulations, and here I was happy with my 95% :)

I had 99%. I was barely off on the bird. After the bird I said screw it with Australia and the USA and barely tried and still got 50/50. LOL

I did best when I didn't "overthink". I would briefly reasoned about the geometry, then stop once it felt right

I got 92%, I’m proud.

I did best when I worked intuitively and fast.

I only got perfect score on the donut/mug one... is this game trying to tell me something?

You are Homer Simpson and I claim my £5, Mr Cthulu_.

Err what are your pronouns, O tentacled horror of an old one (with a trailing ledge).

I got 98% The two I cocked up I spent too long trying to align edges and geometry but actually it seems us humans do have a pretty decent hard wired equal area estimator built in. The last one - AUS/US - should be really hard but I suspect that the results are pretty good.

I'd love to see the results for this. There is almost certainly a decent paper in it.

I got 100pc on the aus/usa, donut and mug, and a few others. Pretty surprised!

Good skills

100% over here, too. I used more geometric thinking at the beginning but of course that shifted into gut feeling by the end. Nice job!

97% (5 perfect). I don't know either. My guess is that most people are pretty good at judging what the half of something looks like. I feel like if the movement (on my phone anyway) wasn't as jerky/sticky I would have gotten one more perfect. I definitely had one that was very inaccurate (55/45) though.

Lol, I got the America/Australia one perfect too! That surprised me!

They seem to be fudging it a bit. In the first example with the circle, anything better than 45%-55% (as measured in my graphics editor) is reported as a perfect 50-50 split.

My main take away is that humans are pretty good at eyeballing 50/50 splits.

Humans are wired to detect unfairness. I bet numerous other animals are too.

https://parentingscience.com/babies-expect-fairness/

Yeah, just imagine the shape is a piece of a pie.

Kids have birthday cake all the time. Believe me they're practiced.

Though they are sensitive to more than the size; they also want the slices with the nice colors and toppings :)

This is a great read. While I'm not 100% sure the method (looking time) is the best, I love how the results are consistent across many experiments. Ofc, the key take away is that it doesn't really matter because personal experiences take over the inherent human "hard wiring".

Two Monkeys Were Paid Unequally: Excerpt from Frans de Waal's TED Talk

https://www.youtube.com/watch?v=meiU6TxysCg

Oh man, that reminds me of the Parable in the bible[1] where everyone gets a full day's wage for as little as one hours work; the workers were fine getting a full day's wage for a full day's work up until those working just one hour got the same at which point they were furious.

1: https://en.wikipedia.org/wiki/Parable_of_the_Workers_in_the_...

There is something weird in our cognitive systems about envy. Wonder why nature "invented" it.

Quite simple if you think of Darwinian evolution - those who get more (and their offspring) outcompete you and your offspring for a limited resource so a resource struggle ensues.

The dynamics of envy leads to individuals segregating, revolting, starving and dying. Is not for nothing that all religions have it as a sin. And I am looking at it with darwinian eyes.

It also makes you think twice before taking more than your fair share, which is the point.

Unfairness deterrence.

You really made me think there.

Thanks for sharing that one.

That idea would imply that homo sapiens (and perhaps other species) instinctually compute possible future dangers of making enemies out of what would be perceived as taking an unfair share. This can trigger a very rich discussion in so many directions. Thanks again for the insight.

Here's some food for thought: https://en.wikipedia.org/wiki/Fair_cake-cutting

I was introduced to this subject through this concise book: https://www.cambridge.org/core/books/evolution-of-the-social...

It's a simple precommitment that avoids huge classes of ways to exploit you. Probably similar to instinctively refusing to pay blackmail even when it's notionally in your interest.

A lot of it probably has to do with competition with siblings too. I know personally that was always a thing with us. We aggressively monitored each others' getting of stuff. I still laugh about it sometimes. So silly but I'm glad people learn this way while the stakes are lower

And comparing sizes of areas in general. There is a small card game called Illusion that is built around that idea.

https://boardgamegeek.com/boardgame/244995/illusion

It would be interesting to see how the ability correlates with social behaviour. Having one or more siblings and the need to share pie, cake, or vlaai probably creates a modest selective pressure.

that time I had to divide my family's coffee mug in half using nothing but a donut really stuck with me

Only tangentially related: There was a great talk about Brilliant's custom diagramming language at last year's StrangeLoop conference: https://www.youtube.com/watch?v=gT9Xu-ctNqI

Funny that this comes up - a lot of times while watching YouTube I'll fidget by trying to highlight exactly half of the title. I check whether or not it's half by dragging the highlighted section over the other half. Glad there's a game for this now!

> check whether or not it's half by dragging the highlighted section over the other half

This is genius, I'm going to do that from now on (and have more reason to be annoyed at the inability to get a perfect split on discrete characters).

92% with 4 perfect cuts (messed up badly on the easy 12-sided shape). Don't know why, but it was a strangely fun exercise. "Brilliant" ad too (pun intended :D)

93% w/ 5 perfect cuts here. :) I now trust my 'visual intuition' more after playing this game! fun experience for sure!

What's interesting is I found that the less time I spent on an estimate the more accurate I was. (5 perfect cuts, 97% accuracy total.)

5 perfect as well (95% total), what does this mean??

5 perfect gives you 100% on those 5 attempts but then your overall % is calculated based on at what margin you missed out on other attempts. ex: if you got 42% instead of 50% in an attempt then that would impact your overall %.

I hope nobody make a captcha out of this, I failed hard

I think it would be a bad captcha—it is impressive how good some people are at this, in the sense that it is surprising that people can just eyeball areas very precisely, but a computer could really easily count the pixels.

What a great ad. Its like its trying to sell brilliant subscriptions via the shareware floppy model.

Many people are saying they did very well, but if I were trying to sell a service I'd tell people that same thing. "Sure, you did a lot of these perfectly, want to do more games that will feel satisfying" seems like a great onboarding strategy.

I was able to get the first five exactly with a bit of luck and think with a bit of thinking it should be possible to always land near 1% or 2%. But is there a good way to cut the cup, bird or map one without calculating it? I got lucky and got the cup exactly but I don't think I could get close without just beeing lucky on the bird and map onea.

The cup is symmetrical and so is the donut shading, so the trick is to flip it on its head: instead of cutting the cup with the donut, cut the donut with the cup by ensuring either the top or bottom half of the donut overlays the cup. With that line of thinking I get a perfect split every time.

No insights to share on the other ones, though.

Oh that is clever, I eyballed it from the left side, but your method makes logical sense. Just tried it and easily got it exactly.

That only works if the cup and donut have the same area.

I believe you, I don’t know. Show me different areas for both and maybe instinct will suggest something different. As it is, and because this was a game, I went for what seemed like a logic-y puzzle-y solution.

But they don't have the same area. The donut seems to be at least 1.5x larger than the cup (check out the screenshots posted by latexr in another comment. The area covered by the donut is half that of the cup but it's clearly less than half that of the donut, it looks more like a third or even a quarter of the donut)

Can you explain more? (I might be stupid and don't see some obvious proof of why your approach is correct), but intuitively it doesn't seem that the fact that the cup is symmetrical is enough. Say if the handle of the cup was really really big, while still preserving symmetry, then its outstanding area would be huge compared to what the doughnut could cover.

> Can you explain more?

https://i.imgur.com/yE43nun.png

https://i.imgur.com/NTfbt5U.png

Note how the middle of the donut aligns with the bottom or top of the cup.

> don't see some obvious proof of why your approach is correct

I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.

Thanks for the reply and for the screenshots. before writing my initial reply, I went back and tried to get a 50/50 split based on your comment and came up with the same solution. But I didn't understand why it worked. I now believe it's either pure luck, or there's something about the sizes that result in a 50/50 split.

I think it's easy to see that if the central hole of the doughnut were either smaller or larger, or if the handle of the cup was smaller or larger, these splits would not work.

> I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.

Sure, that's fair, it's just that your original explanation for how the solution is to swap the problem from splitting the cup to splitting the doughnut was so intriguing and puzzling that got me curious.

With the cup, I moved the doughnut up from below, and just eyeballed when the area above the midline of the cup equalled the area in the hole. Turns out I can do this fairly accurately.

I didn't put much effort into it, and I got pretty close. However, I noticed that I always favored more on the right hand side.

I wish there was a leaderboard or percentile you could see without making an account.

I nominate your comment as the start of the leaderboard. :)

I got 91% overall with 3 perfect splits.

Yeah I’m quite curious what a “good” score is, I thought going into it that it’d be quite hard, but I got

97%, 5 perfect.

94%, 6 perfect cuts. God, I mean, we (humans) are pretty good to cut things in half !

96% accurate, 4 perfect

80% accurate, 2 perfect!

93% accurate, 4 perfect.

95%, 4 perfect. Worst score was 42-58, on the maps one.

Got 99% perfect, 6 perfect cuts, on my first attempt. A couple of the perfect ones, I thought I'd be close, but was surprised to be perfect.

I got 98%, 6 perfect cuts on my attempt. The bird and the plus tripped me up. The bird seems the hardest based on the comments

Same. The only one I missed was the donut/mug.

92%, 2 perfect.

96%, 5 perfect. i went by 'balanced vibes' most of the time.

There were some that had exploitable geometry, but I was surprised to get some perfecta on vibes alone. I think, the star one in my case.

95% 4 perfect

92%, 4 perfect

A leaderboard would be pretty cool. I had tried this a few times and it's the last two that get me. Curious to see how good people are at those.

96%, 5 perfect cuts!

96%, 3 perfect!!

92%, 3 perfect

(I got the bird perfectly, to my surprise. Australia/US I bodged completely.)

I think they should invert Australia, would make it easier.

If anyone wondering on these scores, it is possible to go below 90% ...

Just tested, and it is possible to get 0%. Yet the message will still say “not half bad!” I guess they’re technically correct, it was completely bad.

https://i.imgur.com/ESLd1WV.png

95%, 6 perfect cuts (cut the 2nd one really terribly)

94%, 4 perfect. I feel like the score should also be timed... In hindsight I should have spent more time on some of these!

97%, 4 perfect.

I wonder if the mug & donut reference was intentional

What was it in reference to?

The old joke that mathematicians can't distinguish a donut from a coffee mug (because of topological "equivalence"/homeomorphism) [0]

[0] https://en.wikipedia.org/wiki/File:Mug_and_Torus_morph.gif

To a topologist, a mug and a donut are the same shape (can be deformed to a torus without changing topological properties)

Could be a reference to Dunkin' Donuts

There's no way it wasn't, I laughed when I saw it

How is the area computed? Are they counting pixels?

Constructive solid geometry, and then some sort of computer graphics algorithm for area?

Or is it an SVG, and they're doing some sort of complex integral? (<--probably not)

I'd guess SVG. It's not a complex integral. They can do a boolean intersection in SVG.

They are probably counting pixels but you could for example use destination-out compositing operation on canvas and resize to 1x1 pixel and read brightness of single pixel.

I had to check. It's Next.js /React and the images are all CSS using Chakra. Just looking at the payload, it's sending the byte sizes which tells me they are counting bytes and checking for the difference. Pretty clever.

Is it fudged somehow? The number of perfect cuts we're all getting feels very unlikely to me.

They do appear to be fudging it. At least for first practice example with the circle, it appears to show a perfect 50-50 split when you're up to 5% off (in area) in either direction.

I'm shocked at how little skepticism there was in this thread.

I verified this too. Took a screenshot of a perfect score on the circle, flipped it, and overlaid it. I was 10+ pixels off.

This was probably the best thing in the latest b3ta newsletter (one of those bizarre Barley-esque hangovers from the British internet circa 2004) https://b3ta.com/newsletter/issue880/

Alright. Fat-arms.

This reminds me of NTK.

Is there any proof that doing this regularly helps with anything? Not necessarily making one 'smarter', but at least keeping dementia at bay for older folks? All I could find is that playing board games seems to help with cognitive decline, but this could also be the social part of it.

Physical exercise is the thing that prevents cognitive decline the most.

Six perfect cuts and two 53-47 splits (#6 and #8). For some shapes I was pretty analytical; for example #2 has 21 small squares, so I tried to first cover 11 squares then move it upward by a fifth of the unit. This approach apparently didn't work well for irregular shapes.

The game should remind you in some way which round was which when it shows you the score at the end.

I'm not able to move the white shape.

This might not have been tested on desktop Firefox.

FWIW it worked for me with Firefox 118.0.2 on Windows 11

118.0.2 on Windows 10.

However, I figured it out; interaction with Dark Reader extension.

Turning off the Dark Reader plug-in made it work for me on FF

Did not seem to work with Firefox mobile for me. All I could do is continue without dragging. Turns out you get a score of 26% that way and a rating of "not half bad".

Congratulations! This is really well done - I love the concept and the UX! Beautiful job friend!

I was kind of surprised how good I (and a quick skim of the comment shows, most other people) are at this.

Conventional wisdom seems to suggest that people aren't terribly good at comparing volume when shapes differ, but perhaps that's only in three-dimensions.

Edit: 98% btw.

There is a good amount of gratuitous rounding tbf +-5% at least

I wonder if growing up with similar-aged siblings gives you a natural advantage at this game.

I was 95% accurate! ⬜ Can you do better? https://www.brilliant.org/challenges/halfsies

I was 96% accurate! ⬜ Can you do better? https://www.brilliant.org/challenges/halfsies

94% accurate with 4 perfect cuts. Biggest screwup was the last one, the rest were very close.

Fun game. Could easily see a more robust version of this with 50-100 levels doing pretty well.

Some time ago there was this other game where you have to construct geometrically various points, lines, etc. Does anyone remember the name?

Euclidea?

Thanks. I tried the game in a webbrowser and Euclidea only seems to support native mobile. So there must be another version out there.

As someone who's interested in UI / UX, I have to say, Brilliant is one of those companies whose design is basically perfection.

Would be good though if they had tested it with slightly older desktop Firefox. FF 113 on Linux, which really isn't that ancient, and I can't move the white area.

wow, I was pretty proud of my 88% but then I saw all the comments here

Really neat way to advertise Brilliant. Reminds me of Google Doodles or something.

Is this meant to work on desktop with mouse?

Yupp, worked for me

for some reason it wasn't working before, but it works now.

Touch doesn't work on Firefox Android?

Just played through the first 8, touch works fine on Firefox for Android on Pixel 4a, ver 118.2.0 in About Firefox pane.

That’s a fun little web game. But isn’t brilliant supposed to be educational? This is not at all.

As far as self-study is concerned, it is closer to entertainment than to education (and ultimately just an ad for brilliant.org).

But it is a great educational tool for e.g. a classroom or a math circle led by an experienced mathematician.

Discussion about why these puzzles are solvable and when, and how you can build your own, naturally illuminates concepts such as the intermediate value theorem, simply connectedness, and even measure.

I bet if you did 100 of them you would get pretty good at it.

I can't believe I got perfect on the Mug and America ones! 88%

3 perfect cuts. Only 1 cut below 95%. Seems a bit off

98% and 6 perfect cuts. I blame sibling rivalry.

98% I don't buy it I'm not that good.

Does this use Computational Geometry?

96% accuracy 4 perfect cuts

I'm a halfsize hero

95% Accuracy, 3 Perfect cuts

interesting, i got a few of the trickier ones a littler off...

I was 95% accurate! ⬜⬜

96%, really proud of that

Super cool!!!

I was 93% accurate! ⬜⬜ Can you do better? https://www.brilliant.org/challenges/halfsies

I win

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