This is a long story and it has not finished yet. \par Watson, in 1918, found that $n=24$ is the only integer (except 1) for which the sum of $1^{2}+2^{2}+\dots+n^{2}$ is a perfect square, namely this is $70^{2}$ if $n=24$. Thus arises the next question: Is it possible to pack the squares of sizes $1\times1, 2\times2, \dots, 24\times24$ into a big square of size $70\times70$ without overlapping? This is not an easy question. It was proven only in 2010 that such a packing is not possible; however, the proof is a computer-aided proof. The present paper tries to establish a possible way to build a purely mathematical proof. Many interesting properties of the problem are shown, and much of the work is done, but the proof is not yet complete (the authors do not claim that it is complete). So the question is open for the interested reader.