MHB Divide a big cube into 49 small cubes

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To divide a large cube into 49 smaller cubes, first divide the large cube with a side length of 1 into 343 smaller cubes, each with a side length of 1/7. From these, 336 cubes can be combined to create 42 cubes with a side length of 2/7. This results in a total of 49 cubes, consisting of 42 larger cubes and 7 smaller ones. The discussion also references the OEIS sequence A014544 for additional insights on cube dissection. The method effectively demonstrates a systematic approach to achieving the desired division.
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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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See A014544 - OEIS for information about the number of sub-cubes into which a cube can be dissected.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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