Batch 2 - Class 293 - Pentominoes

• (Geoffrey - 64) As soon as the news of bank robbery came in, a police car was sent to High Street bridge. The robbers had made their escape in a car, and the bridge was the only point of escape north of town. The police car took strategic position at point A on the map. Three patrols were assigned to patrol A-B, A-D and A-C, each going back and forth the blocks 200mx100m in size, at uniform speed of 10km/hr. All of them started from point A at 4am. On the first occasion thereafter when the three met at the car together, a radio message advised them that the robbers had escaped from south side of town. What time did the message arrive?

• Answer: Each patrol must have run 72 lengths of blocks, i.e. 14400 metres when they first get together. At 10km/hr, this means about 1:26 hrs, so time must be 5:26 am

• Use any three pentominoes to fill a rectangle of 15 unit area
• Answer: (there are other answers as well) 

  
• Use any five pentominoes to fill a rectangle of 25 unit area
• Answer: (there are other answers as well) 

  
• Can you use the Z pentominoes to tile a plane? X? F?
• Answer:  

  

   

  

   

  
• Enclosure Problem - Arrange all the 12 pentonimoes to form a closed area within them. They must touch each other at a full edge and not just at a corner. What is the maximum area you can get to?
• Answer: There are many answers - Over 120 is great, Below 70 - try again! Here's a 120 answer

  
• Choose 4 pentonimoes to make a 2x copy of any pentonimo (anything apart from V and X can be done)
• Answer: Sample answer for Z 

  
• Use all 12 pentonimoes to make a rectangle (any size: 10x6, 20x3, 15x4 or 12x5). You can also play on https://www.mathed.page/puzzles/pentominoes/index.html and https ://www.transum.org/Maths/Activity/Jigsaw/Pentominoes.asp?Level=1
• Answer: 

  
• https://math.hws.edu/eck/js/pentominos/pentominos.html has a simulator for 8x8

• Make an animal using pentonimoes
• Answer: Many possible. Some here