Tokarev S.i.

Can one of the factorials be erased from the product $1!\cdot 2!\cdot 3!\cdot \ldots \cdot 100!$ so that the product of the remaining ones is a square of an integer?
$1! \cdot \ldots \cdot 100! = (1!)^{2} \cdot 2 \cdot (3!)^{2} \cdot 4 \cdot \ldots \cdot (99!)^{2} \cdot 100 = 2^{50} \cdot (1! \cdot 3! \cdot \ldots \cdot 99!)^{2} \cdot 50!$. From this, it is clear that, by removing 50!, we will obtain the square of the number $2^{25} \cdot 1! \cdot 3! \cdot \ldots \cdot 99!$

## Answer

It is possible.