What is the Infinite chocolate bar paradox?

In this brief article, we will answer the question, “What is the Infinite chocolate bar paradox?”  and provide information on whether you indeed obtain an extra chocolate block, how to conduct the experiment on a 5 x 5 block as well as the number of times you can conduct the experiment.

What is the Infinite chocolate bar paradox?

The infinite chocolate bar paradox consists of a geometric illusion wherein you seem to obtain an extra block of chocolate from a single chocolate bar.

For conducting this experiment, you would need to have a 4 x 6 chocolate bar and a butter knife.

If you wish to conduct this experiment, first cut the chocolate bar diagonally from the top corner starting from the third block of chocolate. 

The cut should extend to the bottom corner of the third block. Cut the fourth column of the chocolate bar. The fourth column of the chocolate should have 4 squares of chocolate. You would now have 3 pieces of chocolate.

The previous top corner of the chocolate can be labeled as A, the thin bar of chocolate (fourth column) can be labeled as B whereas the remaining portion can be labeled as C.

Swap the position of the chocolate pieces. The chocolate piece B can be kept in place of A and A can be kept in the place of B. There is no change in the position of C. You might think that you ended up with an extra block of chocolate.

What does infinity mean?

Infinity refers to a term that can be used to refer to anything unlimited. This can refer to objects, space, time, distance, numbers, etc. The symbol ∞ is used to denote infinity.

Do you really obtain an extra chocolate block?

No, you do not obtain an extra chocolate block. It is simply a geometric illusion. You can count the number of blocks or squares in chocolate before and after the experiment. The number will be the same.

Use a ruler and measure the length of the chocolate bar. You will notice that the chocolate seemed to be smaller than before the experiment. Every time, the chocolate is cut and rearranged, the chocolate’s length would keep getting smaller. 

As a result, there is no extra chocolate. In fact, there is lesser chocolate than before but as the width of the chocolate seems to be bigger, it appears that there is an extra block of the chocolate present.

How can you conduct an Infinite chocolate paradox experiment on a 5 x 5 chocolate block?

Take a picture of the chocolate before cutting them. If you have a 5 x 5 block, start to cut the chocolate from the right-hand side in a diagonal manner a little above the third block. The cut should end on the left side and it should be slightly below the second block.

Let us label the first top block obtained as A. Now, slice block A in a linear fashion from the left. The cut should be slightly below the third block. This piece can be called B. The remaining piece can be termed C.

From piece B, you need to obtain two more pieces from the first row. Chop a small square from B which can be called D and the remaining two pieces from the row need to be cut off too. 

This 1 x 2 rectangle is called E. The remaining portion of the chocolate bar B has to be called F for convenience.

Now, it is time to rearrange the chocolate pieces. Keep the picture of the chocolate you had previously taken and keep them beside you to not get confused.

Move the piece of F to the right. Keep piece C in the area where F was initially kept. In the space above C, keep piece E. The extra block of chocolate is obtained (This is actually block D). 

You can repeat the same steps as above to get an extra block of chocolate. However, the length of chocolate will keep reducing. 

How many times can you conduct the Infinite chocolate paradox?

You can conduct this experiment only a limited number of times. Even though the experiment calls itself infinite, you will soon run out of chocolate as the length of chocolate keeps reducing after every experiment.

What is the Infinite paradox?

According to the Infinite Paradox, Infinity behaves like a number even though it might not be one. You can subtract or add numbers to infinity but the result remains the same. The Infinity chocolate paradox might be inspired by the concept of the Infinite paradox.

Conclusion

In this brief article, we have answered the question, “What is the Infinite chocolate bar paradox?” and provided information on whether you indeed obtain an extra chocolate block, how to conduct the experiment on a 5 x 5 block as well as the number of times you can conduct the experiment.

References

https://www.smorescience.com/infinite-chocolate-bar-paradox/

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