A simple geometry question that fools almost everyone

https://www.theguardian.com/science/2025/feb/17/can-you-solve-it-the-simple-geometry-question-that-fools-almost-everyone

by mywacaday • 1 year ago

16 14 1 year ago

theguardian.com

mywacaday2• 1 year ago

The solution is available if you look but this one gave me a good chuckle to myself.

madcaptenor• 1 year ago

I was very happy with myself for seeing the first trick... but fell for the second trick.

avandekleut• 1 year ago

I started with cosine law and then went "wait a minute" - but still jumped to the wrong answer as pointed out in the solutions.

randcraw• 1 year ago

Their answer to the first question is actually wrong. The correct answer is 1 less than the given answer.

mywacaday2• 1 year ago

I thought that initially but their answer is correct.

echoangle• 1 year ago

SPOILER AHEAD:

Why? You're still measuring the distance between the two points on the line. One is in the middle and one is not.

hnuser1234562• 1 year ago

Given the (required) note that the misleading set of "triangles" is not drawn to scale, there is a range of solutions between 1 and 5.56776, since the angle of BCD is not specified to be 180 degrees (just as angle BAC is not given)

You could instead fold up the lines connected to the D point, into a V shape with the D point at the bottom, such that the points B and C (the top tips of the V) are separated horizontally by length 2 (and vertically by 0), and use the length 5 and 3 sides to go 4 units straight left or right from the top center of the V, and place point A and connect back to the far side of the V. Now point A is 3.87298 units above and 4.0 units to the side of point D, a diagonal length of 5.56776.

You could continuously deform this shape back down to the straight line case.

Now that I think about it, in the process of that deformation, there might be a point where slightly widening the V would allow you to place the point slightly higher and get an even larger max distance.

thomasahle• 1 year ago

It's like that Amazon Hanging Cable Interview Question

idoubtit• 1 year ago

I solved it, to my own surprise, by considering a more general problem. I wanted to get an interval for the solution, so I replaced 3 with y. Now for y=5, the solution is obvious. x(y) is a increasing function and its minimum is... oh!

laserbeam• 1 year ago

This… feels like one of those “99% of people can’t do this basic math trick” memes. I mean, yeah, the puzzles are actually cool, but it feels strange to see such posts on a news website.

dgeiser13• 1 year ago

What news site? Hacker News or The Guardian?

SirMaster• 1 year ago

Not sure why this is supposed to be hard. Apollonius's theorem works as it's intended to here.

AB^2+AC^2=2AD^2+2BD^2

https://www.wolframalpha.com/input?i=5%5E2%2B3%5E2%3D2x%5E2%...

A simple geometry question that fools almost everyone

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