Batch 2 - Class 75 - Pentominoes (Spatial Visualization V)

Preclass Exercise:

Attendance: Smiti, Muskaan, Tishyaa, Aryan, Adit, Liza, Nandini, Praharsh, Khushi

Class Notes:

Pentominoes are shapes made by joining 5 unit squares along the edges. Following are the kind of pentominoes and their labeling.

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

Homework

Use all 12 pentonimoes to make a rectangle (any size: 10x6, 20x3, 15x4 or 12x5)
Answer:
Arrange numbers 1-32 in a circle so that any two adjacent numbers sum to a square
Answer:
3D Tic-tac-toe Competition - Download the 3D Tic-tac-toe game on your phone/online (https://www.mathsisfun.com/games/foursight-3d-tic-tac-toe.html) - Note that this is a 4x4x4 tic tac toe game.

References: