Batch 2 - Class 320 - Slippery Snail, Silver Dollar and NIM Games

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Preclass Exercise:

(In class)

Attendance: Anika, Yatharth, Vansh, Kabir, Aarushi, Adyant, Vivaan, Ekagra, Savya, Aneesh, Tarush, Ayush, Rhea, Ryan, Aarav, Advay, Nikhil

Class Notes:

Recap slippery snail

With 4 bugs in slippery snail, we saw those as two sets, and like two piles of stones from which we are taking away a few. As long as we could keep the distances between bugs in each set the same, we can win
What if there are 6 bugs?

Silver Dollar

https://wild.maths.org/silver-dollar

Let kids play a few games
What is the winning strategy
Do you see parallels between this and the slippery snail game?
Talk about equivalence of problems, and its applications, for example in NP hard problems like traveling salesman, graph coloring and halting problem (https://en.wikipedia.org/wiki/NP-completeness)
What if there were 6 steps to the ladder?

Stone piles

Play the game where there are two piles of stones, and a player can remove any number of stones from one pile. The player who finishes the stones first wins
Do you see the parallel between the slippery snail and silver dollar games?
What if there were 3 piles of stones?

In 2 piles, making the piles equal represents something in binary math. What is it?
Can we extend that to 3 piles? If required play the game with students couple of times, and ask them to write the binary representations of numbers in each pile. See if they observe a pattern to your moves
The trick is to make the binary sum 0000. Same thing that we were doing in two piles

Now can we extend this solution to slippery snail and silver dollar?
What are the differences between the stones and slippery snail problem that are important to consider? Establishing equivalence has to be a thorough exercise!

Homework:

(536Dudeney - 319) The fly at point A below take a minute to crawl an edge of the cube. How long will it take it to reach point B?

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