You are planning a haunted yard for Hallowe’en. You have a lot of what you require already, but money is tight. You have $20 to spend. You have come up with a list of scary stuff with each item’s cost and scariness (per occurrence):
– haunted doorbell (one only): $3, 2 scary points
– tombstone: $2, 1 scary point but doubled if 5 or more tombstones
– scary tomb: $10, 5 scary points
– vampire figure: $15, 5 scary points
– vampire costume and makeup: $10, 10 scary points
– small, carved pumpkin: $3, 1 scary point
– large, carved pumpkin: $5, 2 scary points
You do not want an insipid haunted yard so it must have at least three items and at least 20 scary points.
How many different haunted yards can you come up with if you do not repeat any items? How about if you can repeat items as much as you can afford (except for the one marked “one only”)? (You do not have to spend all of the money.)
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 5, 2014 at noon Pacific Time. I will post the answer shortly after.