This is question from my college math test for JEE . In this question we are asked to find the missing digits of 19!. I skipped this question in my test but I tried it after the test and I made many errors while calculating it. Is there any way i can find the missing digits within 2 minutes since we are expected to do 60 lengthy and hard (like the above one ) questions in 2 hours.
I would like to thank you for helping me to solve this problem .
$19!$ is multiple of $1000$ so it has to finish with three $0$'s. So $H=0$. Also $19!$ is multiple of $9$, and of $11$, using the criteria for divisibility by $9$ and by $11$ you can find some equations satisfied by $T$ and $M$.