Sorry about the double post if some of you are reading both sections but I was unsure where this could go, so I decided to ask in both.

Here is an interesting proof (in my opinion) maybe some of you will have some insight. I have managed to prove it but in a long and non efficient way. Here's the proof:

We have 1!*2!*3!*4!*5!*6!...*100!

Prove that you can eliminate one factor so that the remaining number is a perfect square.

What I have done is using the help of a computer prime factor each number 1! through 100!, then added their powers and from that I saw that by eliminating 50! the number 1!*2!*3!*4!*5!*6!...*100! will have its prime factorization all to an even power, resulting in a perfect square. Now I am sure there should be a more efficient way in doing this, any help?