## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewestInfinite chocolate! Time for Willy Wonkers to research into it :) – Calvin Lin Staff · 3 years, 2 months ago

Log in to reply

The cutting line is not a complete straight line.

missing square = the difference between the actual straight line and the cutting line in this problem – Ossama Ismail · 3 years, 2 months ago

Log in to reply

\[ \left| \begin{matrix} 0 & 3 & 5 & 0 \\ 2.5 & 3.5 & 4.5 & 2.5 \\ \end{matrix} \right| = 1 \]

(The above is known as the shoelace formula. You can calculate it the old fashioned way if you are unfamiliar with this.)

This accounts for the additional piece of chocolate.

YUM! – Calvin Lin Staff · 3 years, 2 months ago

Log in to reply

– Kou$htav Chakrabarty · 3 years, 2 months ago

It seems so.Log in to reply

– Naimish Khara · 3 years, 2 months ago

right...Log in to reply

If you will see with full concentration at it you will found that the pieces of the block containing 3 rectangles has base which will gradually increases as it moves up you can see it by focusing it's a nice trick – Rohan Kumar · 3 years, 2 months ago

Log in to reply

– Maharnab Mitra · 3 years, 2 months ago

Yeah! You're right! Great observation.Log in to reply

The way it was cut diagonally resulted in a gap so small you can't visibly see which amounts to the "left over piece". – Venture Hi · 3 years, 2 months ago

Log in to reply

I think if we analyze by taking screenshot of each section we can find that the shape at the edges is not correct after they connect .They changing the shape while connecting it again.

I have taken screenshot and attached in the following link.U can check the same and analyze. http://www.ltewirelesstech.com/2014/03/just-see-carfully-and-analyze.html – Sachidananda Sahu · 3 years, 2 months ago

Log in to reply

never thought of this wooow.. – Tootie Frootie · 3 years, 2 months ago

Log in to reply

I have a feeling that the diagonal line is being cut in such a way that \(\frac{1}{5}\) of each small piece/cell of chocolate involved in the cut is being added again, thereby making the whole chocolate cell adding process quite inconspicuous.

I'm probably wrong though. – Milly Choochoo · 3 years, 2 months ago

Log in to reply

– Calvin Lin Staff · 3 years, 2 months ago

That's actually very close to the truth! It's not a diagonal line that is being cut out, but more of a thin triangle.Log in to reply

This is merely a corollary to the Tarski-Banach Theorem, of course there's nothing funny going on here. If one can decompose a sphere and make 2 spheres, each the same size as the original, from it, surely we can make an extra chocolate piece here. – Michael Mendrin · 3 years, 2 months ago

Log in to reply

Seeing is not believing. – Calvin Lin Staff · 3 years, 2 months ago

Log in to reply

– Michael Mendrin · 3 years, 2 months ago

Calvin, can't you see a joke? Bringing in the Tarski-Banach Theorem is like bringing in a flame thrower to kill a fly. Others here have already correctly identified the problem, kudos to these folks.Log in to reply

What do you think is the best way of explaining exactly how the Banach Tarski paradox works? – Calvin Lin Staff · 3 years, 2 months ago

Log in to reply

This theorem does depend on the "Axiom of Choice", though, it presupposes that given any infinity of non-empty sets, it's always possible to create a set which contains exactly one element from each of those sets. This might seem obviously true, but, like the parallel postulate, nobody's been able to prove this. – Michael Mendrin · 3 years, 2 months ago

Log in to reply

its nothing but a illusion that if go no to a series we come to first row last second piece (which is cutted half) while sliding(moving up) it increases in its size. I HOPE YOU WILL GET IT. – Kshitij Karale · 3 years, 2 months ago

Log in to reply

Actually the size decreases! – Vasavi GS · 3 years, 2 months ago

Log in to reply

– Daniel Wang · 3 years, 2 months ago

or so they say.Log in to reply

– Kou$htav Chakrabarty · 3 years, 2 months ago

But how? Ossama Ismail above also gave a possible way it decreases but still I haven't got it in my headLog in to reply

my Brain si Bleeding... – Chaidir D'dalz · 3 years, 2 months ago

Log in to reply

The part which is cut from right and fitted into left, will not fit exactly because that is less than what was cut from left but it is depicted so in the animation and same thing for right side. and hence the additional piece of chocolate will not be there in reality – Govind Sharma · 3 years, 2 months ago

Log in to reply

it is like the shifting of origin of perfect square – Roshan Kulkarni · 3 years, 2 months ago

Log in to reply

Wow.......Can it be really happen?? – Monirul Haque · 3 years, 2 months ago

Log in to reply

how can I post a picture????? – Rohan Kumar · 3 years, 2 months ago

Log in to reply

(look here)option when you share a problem or note. – Kou$htav Chakrabarty · 3 years, 2 months ago

There's a 'attach image'Log in to reply

– Rohan Kumar · 3 years, 2 months ago

no in the comment boxLog in to reply

It has many choclate or uncountable choclate!!!!!! – Tejashv Chaturvedi · 3 years, 2 months ago

Log in to reply

if you see with concentration you will find out that it is not possible, as size of pieces are not equal... – Naimish Khara · 3 years, 2 months ago

Log in to reply

– Maharnab Mitra · 3 years, 2 months ago

I also observed it. Clever trick!Log in to reply