This one comes courtesy of Mystery Fred. The diagram above is for a Circle Gaps Brainteaser, and appeared online last week as part of Double Helix, CSIRO‘s science magazine for kids. The text for the brainteaser (as if it matters) is as follows:

*What is the area of the orange star in the centre? The blue circles each have an area of 3 square centimetres, and the big square has sides that are 4 centimetres long.*

A comment on the post makes it clear that the choices of sidelength and area were purposefully made.

Wow, that’s amazingly stupid.

I wrote this, but it probably won’t make it through. I was trying very hard to be nice enough but probably won’t be enough.

CSIRO declares pi equal to 3!

Not good enough, folks.

“Anonymous

2 May, 2023 at 10:38 am

This is miserable. The circles are slightly smaller than required to give tangency. Pi =/= 3.

So, we don’t know the area of the orange. We don’t know if the circles are smushed together towards the center or spaced out to the edges.

Bad puzzle.

Your comment is awaiting moderation.”

Reminded me of the following. V.I. Arnold, in his famous “Problems for Children from 5 to 15”, gives the problem from his life experience:

Problem 6

The hypotenuse of a right-angled triangle (in a standard American examination) is 10

inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.

American school students have been coping successfully with this problem for over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why?

I wonder how many people checked this ‘brain teaser’ before it was published and thought it was ok….

Hi,

In the unlikely event it’s not a proof readers typo from a high school magazine then perhaps it is a non Euclidean surface?

Disks on planes grow more quickly with radius than disks on spheres for example

https://math.stackexchange.com/questions/1832110/area-of-a-circle-on-sphere

Steve R

That’s *really* hunting hard for the pony.

It’s not a typo. The comments after the puzzle make it clear that the authors were aware that the puzzle didn’t work.

Marty,

sorry for that

As compensation here is a lateral thinking circle puzzle#217 from the new scientist a couple of weeks ago about a flesh eating monster in a circular moat

Puzzle #217: Vicious circle

regards

Steve R

An engineer created this puzzle.

SRK

Not sure as I only read the magazine but the solution only requires a little bit of thought , a couple of assumptions and knowledge of the circumference of a circle of radius r

Steve R

Steve, not sure I’m understanding your comment, but I was just making a reference to the old joke that engineers often use the approximation

SRK

Sorry I have an offspring studying

Engineering so I’ll test the joke on her

I know they use j for the square root of -1

because i is used for current (;)

Steve R