Fox 349

This is just one step forward to the general case. Should not be very hard unless the claim is wrong :)

Yes, a geometric solution will be appreciated...

Fox 348

We'll return back to Sampy's question later. But, for a change let's see a simple one - or at least it looks simple. We're looking for the shortest proof of the claim below. May be purely-geometric one? Or is the claim wrong? Let us know...

Fox 236 - Solution-1

See the original problem: Fox 236

http://www.8foxes.com/

Let simplicity ring all accross the land...

Fox 250

http://www.8foxes.com/
Bleaug submitted this one, saying that he got inspired by Yu's elegant solution to Fox 246. More is on the way...

Fox 242 - Counterexample-2

Yu claims:
A rectangle is a trapezoid. The shaded area (2 equal triangles) = ¼ of the rectangle.


The above trapezoid has the same area as the rectangle above. As P approaches Q, the height of the upper shaded triangle increases faster than the height of the lower shaded triangle decreases. .: the shaded area > ¼ of the trapezoid.

Fox 242 - Counterexample

http://www.8foxes.com/

Bleaug has submitted this counterexample. He smells right :)

Easiest way is to get a counter-example:
assume the upper side of the trapezoid collapses to a single point,
the pink area corresponds to 1/4 of the trapezoid/triangle area.
The (non-empty) blue area is in excess.

Fox 242

http://www.8foxes.com/

A nice counterexample was found!

Fox 221 - Solution - 2

http://www.8foxes.com/

Fox 241

YES, the solution has NOW been confirmed!!

We will post these excellent solutions here later!

There are at least one more slick solution, not identified yet!

Thank you guys for the great work!

http://www.8foxes.com/

Fox 239

http://www.8foxes.com/

Make things as simple as possible, but not simpler.

Fox 237

http://www.8foxes.com/

Fox 236

http://www.8foxes.com/

There should be several purely geometric solutions.

Fox 228

http://www.8foxes.com/

Fox 226

A general version of Fox 226 is submitted by Ajit. Enjoy!

http://www.8foxes.com/

Fox 219

Fox 195

http://www.8foxes.com/

Fox 170

http://www.8foxes.com/Home/170

Fox 169

What is their story?
What is your story?
You know what they are.
Do you know who they are?

Fox 153

Think simple.
Math has nothing to do with numbers.
Try to see the connections.

http://www.8foxes.com/Home/153