## Keep your brain fit – there’s no such a thing like free lunch!

### I noticed Chocolate Bar Trick going viral lately. In case you did not spot it, it goes like this: you have a chocolate bar, 6×4 squares in this example, you extract one square from the chocolate, you cut and rearrange remaining 23 chocolate squares, and, voila!, you magically again have all 24 squares at your disposal!

If it was that easy, you’d need to purchase one single chocolate and it lasts your entire life; you’d just need to carry a knife with you… Of course, there’s no such a thing like free lunch, so let’s unmagic the magic of infinite chocolate bar.

But first, let’s have a look at original video, in case you missed it before:

At first, I thought the missing square was lost in uneven cuts between segments, it looks like slopes of two cut pieces do not join tightly. Upon closer examination, though, it is easy to spot where it is: as you slide two bigger pieces along the cut line, the height of chocolate bar (the one that measures 6 squares) decreases, so although you can again count 6 squares after rearrangement, the bar height is definitely smaller!

Let’s recreate it with a paper, it’s easier to see. Here is our paper chocolate.

As you can see, it measures 6 x 4 squares. If using background grid on the paper, dimensions of each square are 4 x 6 units. Hence, area of a single square is 24 units, and total area of our chocolate is 576 units. Here is the cutting line and “extra” square.

Just for double check, let’s measure our chocolate before cutting it: it’s width and height are equal, and amount to 120 mm (paper grid dimensions are obviously 5 x 5 milimiters).

Let’s cut our chocolate.

Rearrangement fits nicely, the slope is even and three pieces fit back into a perfect chocolate bar made of 6 x 4 = 24 squares, and we have another spare square, so did we just made 25 squares out of 24?!

Yes, we did, but if you take a closer look, you will see that row where we made the cut is now lower: instead of initial 4 units, its height now is only 3 units!

So, we have 5 rows with 4 units height, and 1 row with 3 units height. Width of each row has not changed, it remained 24 units, so total area of new chocolate bar is (5*4 + 1*3)*24 = 552 units. The difference between initial 576 units and 552 units at the end exactly equals to one surpluss square!

Let’s measure it again to confirm we found a culprit:

Indeed, instead of initial 120 mm, height is 115 mm now, allowing for one missing row, which equals to one square of chocolate bar!

Hope you liked the puzzle and solution! What at first seemed as mistery, has simple and logical explanation! π Let us know your thoughts in comments below, and enjoy your day! π

Cover photo on main blog page by *Brigitte Tohm @ Pexels*

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