**Conjecture**For any integer , it is impossible to cover a square of side greater than with unit squares.

Alexander Soifer in [S] raises the question of the smallest number of unit squares that can cover a square of side . He shows the asymptotic upper bound , and the small values , , and . He conjectures the asymptotic lower bound .

## Bibliography

[S] Soifer, Alexander, "Covering a square of side n+epsilon with unit squares," J. of Combinatorial Theory, Series A 113 (2006):380-383.

* indicates original appearance(s) of problem.