![](/files/happy5.png)
Conjecture For any integer
, it is impossible to cover a square of side greater than
with
unit squares.
![$ n \geq 1 $](/files/tex/89889e1b8de346d344ae13193ac6d9420c272315.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ n^2+1 $](/files/tex/07591b8f5cfcfca6c88922b69bde7a5bee55f3d3.png)
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.