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You are given a piece of cheese in the shape of a cube and a knife.

In order to get 27 small cubes, you need to divide each of the three cube faces into three parts. To reach three divisions, you need two cuts. An obvious solution is to create the cuts parallel to each other across all three axes. In order to make this, you will need only six cuts. 

 

Note! When trying to solve such challenges, the first solution that appears in your mind will not be probably the best one. Is it possible to improve the solution? Keep in mind that you can move the pieces after each cut (chefs often do such things when they cut an onion). It will greatly increase the number of possible solution options and then you will find the best one you have not paid attention firstly at.

 

In fact, there is no actual way that gives you an opportunity to cut the cube into 27 pieces in less than 6 cuts. Ideally, you should prove it. Let’s take a look at the way you can do it. 

 

Imagine a small cube that you have after cutting the initial cube into 3x3x3 = 27 parts. This cube is placed in the middle of the source cube. It does not have a surface that verges upon the external world. For this reason, you will need to create each of 6 sides with the help of a knife. Six straight cuts are the minimum you need to solve this challenge. This task relates to reverse mind-teasers. obviously, the first answer appears correct, although many people try to find out unobvious solution options.

 

According to Martin Gardner, the author of the mind-teaser was Frank Hawthorne, the director of the education department in New York, who published it in 1950. The idea of regrouping parts to reduce the number of cuts is not so crazy as it may seem. In this case, you can cut the cube into 4x4x4 cubes with the help of six cuts (with the previous approach, you would have to make nine cuts).

 

In 1958, Eugene Putzer and Lowen published a general solution for cutting a cube into NxNxN cubes. They assured all practically-minded readers that their method could have “important consequences for the industries producing cheese and sugar cube”.

 

This question vaguely resembles another one that is asked at interviews in some financial institutions: how many cubes are in the centre of a Rubik’s cube? Since such a standard cube consists of 3×3×3 parts, one often gives the wrong answer. However, any person who ever sorted out a Rubik’s cube knows that the correct answer is different – zero. In the middle is not a cube, but a spherical hinge.

 


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