[asy][asy]for(int i=0;i<7;++i){draw((0,i)--(6,i)^^(i,0)--(i,6));if(i<5)label(string(i+1),(i+1,6),N);}[/asy][/asy] At least one domino must straddle the $i$th line. But then there an odd number of remaining squares on either side of the line, so another domino must straddle the same line. Therefore there are at least ten horizontal dominoes. By the same argument, there are at least ten vertical dominoes. But there isn't enough room for twenty dominoes.