This is an extremely interesting question. I have no idea why it works, but there is a pattern.
Here are the values of n that I found that when multiplied by 144 give 144 as the last 3 digits. Notice how the pattern repeats. 26 51 76 01. I only took it up to 1001 because I discovered that without the help of a computer program. Thanks for posting. Nice afternoon to you.
The awnser is 1000 because 60 miutes in an hour, 50 mouse traps every half hour so 100 mouse traps an hour multiply that by 10 and you get 1000, i think.