Batch 2 - Class 88 - Frogs & Toads, Mirror Maze
Pre-Class Problem:
- Consider the stack of dice as shown above. What is the sum of all hidden faces (Note that faces at the back are not hidden)Answer: Any two opposite faces of a dice total to 7. Since opposite pairs of 5 dice are covered, they must total to 35. Similarly the opposite face of top dice must be 6 and 5, so complete total is 48
Attendance: Anisha, Muskaan, Tishyaa, Adit, Diya, Nandini, Liza, Khushi, Arnav, Anishka, Tara, Navya, Avy
Class Notes:
Frogs and Toads
In the above diagram, the frogs (colored brown) can move down or right. Toads (the green ones) can move up or lfet. A frog or toad can slide into an empty adjoining space, or jump over exactly on of the other kind of animal. You need to exchange the positions of all toads and frogs.
- That is probably pretty hard. How can we make the problem easier?Teacher's Notes: Let kids come up with ways of making it easier and let them explore those. Some possible waysReduce to 3x3 center squareReduce to a one dimensional problem - again can do 3 or 5 stripCan you tabulate the number of steps required? How many jumps and how many slides?Can you figure out a way to write your solution?Can you spot a pattern in the slides and jumps?Can you solve a one dimensional problem with different number of frogs and toads on each end - lets try with 2 frogs and 3 toadsCan you figure out the number of steps required?Answer: MN Jumps and M+N Slides
- With the one dimensional middle row solved, Now come back to original problem, and see what happens when you solve the middle row.Teacher's Notes: This problem illustrates the notion of dimensionality very well. See if kids get thatAllow kids time to figure out what is happening as you solve the middle rowCan you count the number of steps required? Can you derive from linear 5 strip answer?
- What if you had a three dimensional grid of frogs and toads now?
Homework
Mirror Maze
Given a square grid, width some squares blocked and some occupied by mirrors, the task is to travel through all the available cells without crossing the itinerary.
The rules are as follows:
- You may not enter a blocked cell, which is filled with a solid square;
- You may enter the square with a thin mirror (shown with a slash or a back slash) twice without crossing the slash;
- You may enter the half solid mirror (shown as a painted triangle) only once through a non-painted part of it.
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Note that you can not hit and reflect off the non-inclined sides of triangle or square. This Puzzle's task is to visit all of the vacant cells of the game field by drawing a closed line which does not cross itself. Example below:
Lets solve for a few:
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Hint:
References: