  A tiling of the unit square is an MTP tiling if the smallest tile can tile
all the other tiles. We look at the function $f(n)=\max \sum s_i$, where $s_i$
is the side length of the $i$th tile and the sum is taken over all MTP tilings
with $n$ tiles. If $n=k^2+3$, it was conjectured that $f(k^2+3)=k+1/k$. We show
that any tiling that violates the conjecture must consist of at least three
tile sizes and has exactly one minimal tile.
