Batch 3 - Class 160 - Topology, Game of Three Musketeers
Pre-Class Exercise
- In the problem above, can you attempt to find a surface where the loop can be closed?
- Answer: If we draw a donut with two holes, each hole capturing one of the rectangles on the shape, that would work. For example a hole through A and B
Attendance Muskaan, Arnav, Anishka, Liza, Siddhanth, Arjun
Class puzzles
Game of Three Musketeers
A board is laid out as under, with three musketeers and 22 enemy pieces. The player with three musketeers starts first, and musketeers can move to any adjacent squares (not including diagonals) with an enemy piece, thereby capturing the enemy. Next, the enemy may move to any empty adjacent square. The game continues. The objective of the enemy is to get all the three musketeers in the same row or column. The musketeers win if its their turn and there is no adjacent enemy to be captured.
Scoring: If the musketeers win, they get 10 points. If the enemy wins, they get points equal to number of surviving enemies on the board.
Play a few of these games, and come up with strategy to win (on both sides).
What if scoring is changed, whereby if the enemy wins, they get 10 minus the surviving enemies on the board?
Cutting Mobius Strips
- Ask kids what would happen if they cut a circular strip through the center
- Answer: Will split into two strips
- Show a Mobius strip
- How many surfaces does the Mobius strip have?
- Answer: 1 (Can demonstrate by drawing a line through the middle)
- How many edges does the Mobius strip have?
- Answer: 1 (Trace an edge using a pen)
- Cutting a Mobius strip
- Ask them to see what happens if they cut it through the center
- Answer: Remains in one piece, twice as long, with twice the number of twists
- Ask them to draw a line about a third along the width and see what happens - Cut along the line
- Two loops - one inside the other, with one and two twists respectively
- Ask kids what would happen if they cut two circular strips joined at right angles
- Answer: Becomes a square
- What if one of those bands was twisted into a mobius strip?
- Still the same square :-)
- What if you trisected the Mobius strip?
- Square with another mobius strip inside it!
Homework Problem:
- (536Henry: Problem 51) "Between two and three oclock yesterday," said Colonel Crackham, "I looked at the clock and mistook the minute hand for the hour hand, and consequently the time appeared to be fifty-five minutes earlier than it actually was. What was the correct time?"
- Answer: The time must have been 5(5/11) minutes past two oclock.
References:
A Gamut of Games, Sid Sackson
536 Puzzles and Curious Problems, Henry Dudeney