What is the largest number of subcubes (not necessarily different) into which a cube cannot be divided by plane cuts? The answer is 47 (Gardner 1992, pp. 297-298). The problem was originally posed by Hadwiger (1946), and Scott (1947) showed that dissections were possible for more than 54 subcubes. This left only 47 and 54 as possible candidates, and a dissection into 54 pieces in 1977 independently by D. Rychener and A. Zbinden resolved the solution as 47 (Guy 1977; Gardner 1992, p. 297).

# Hadwiger Problem

## See also

Cube Dissection, Cutting## Explore with Wolfram|Alpha

## References

Gardner, M.*Fractal Music, Hypercards, and More: Mathematical Recreations from Scientific American Magazine.*New York: W. H. Freeman, 1992.Guy, R. K. "Research Problems."

*Amer. Math. Monthly*

**84**, 810, 1977.Hadwiger, H. "Problem E724."

*Amer. Math. Monthly*

**53**, 271, 1946.Scott, W. "Solution to Problem E724."

*Amer. Math. Monthly*

**54**, 41-42, 1947.

## Referenced on Wolfram|Alpha

Hadwiger Problem## Cite this as:

Weisstein, Eric W. "Hadwiger Problem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/HadwigerProblem.html