You have just seen the grouchy, old man next door’s plans for Hallowe’en. (“I am keeping all of the candy. None for those kids”, he claimed.) He has his sidewalk and porch boobytrapped. (He also has a minefield under his lawn, but that is just part of his normal defences and is not part of this Hallowe’en puzzle. Another time, perhaps.)
He has a total of ten traps along the sidewalk and two on the porch. The traps are, in some order, two pit traps, four trip wires, three snares, and three leghold traps. (“The lawn is actually safer”, he chortled. “But those kids still better stay off my lawn.”)
1) How many different arrangements of traps are there?
2) How many if there must be exactly one pit trap on the porch?
3) How many if there must be at least one pit trap on the porch?
4) Do you have any neighbours like this?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 12, 2014 at noon Pacific Time. I will post the answer shortly after.