Divide a big cube into 49 small cubes

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Discussion Overview

The discussion revolves around the problem of dividing a large cube into 49 smaller cubes. The scope includes mathematical reasoning and exploration of different methods for achieving this division.

Discussion Character

  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant suggests a method where a cube with a side length of 1 is first divided into 343 smaller cubes of side $\frac{1}{7}$, and then 336 of these are used to form 42 cubes of side $\frac{2}{7}$, resulting in a total of 49 cubes.
  • Another participant reiterates the same method, indicating agreement with the proposed approach.
  • A different participant references the OEIS sequence A014544, which relates to the number of sub-cubes into which a cube can be dissected, suggesting a broader context for the discussion.

Areas of Agreement / Disagreement

There appears to be agreement on the method proposed for dividing the cube, but the discussion does not explore alternative methods or challenge the initial approach in detail.

Contextual Notes

The discussion does not address potential limitations or assumptions in the proposed method, nor does it explore the implications of the OEIS reference in depth.

Albert1
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Please divide a big cube into 49 small cubes
 
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Albert said:
Please divide a big cube into 49 small cubes

[sp]You can be assumed to follow a procedure of this type. Il the side of big cube is 1, then You first divide it into 343 cubes of side $\frac{1}{7}$. Then You use 336 of them to form 42 cubes of side $\frac{2}{7}$, so that at the end 42+7=49 cubes remain...[/sp]

Kind regards

$\chi$ $\sigma$
 
chisigma said:
[sp]You can be assumed to follow a procedure of this type. Il the side of big cube is 1, then You first divide it into 343 cubes of side $\frac{1}{7}$. Then You use 336 of them to form 42 cubes of side $\frac{2}{7}$, so that at the end 42+7=49 cubes remain...[/sp]

Kind regards

$\chi$ $\sigma$
very good ! here is my solution
if the big cake of side 6
divide the cake into three lays:
the first lay of side 2 (9 cakes)
the second lay of side 1 (36 cakes)
the third lay of side 3 (4 cakes)
9+36+4=49
 

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Last edited:
See A014544 - OEIS for information about the number of sub-cubes into which a cube can be dissected.
 

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