Batch 2 - Class 84 - Moving Pennies

• (Expii) After a deep hundred year slumber, Ant the ant wakes up in an unfamiliar, large, dark square forest. Ant is unaware of its exact location or direction, but it does know that its starting point is exactly 10 meters away from the nearest straight edge. What is the shortest distance Ant must travel to guarantee escape from the forest? Round your answer, in meters, to the nearest hundredth.

  Answer: Not really sure - let kids describe the best solutions they have been able to come up with

• Six pennies are arranged in a triangular setting. Use minimum number of moves to arrange them in a hexagonal shape (with middle penny missing)

  Answer: Can be done in 4 moves if one wants to know exactly where to position pennies (move middle row to below the bottom, and then center penny and then the top one). Can be done in 2 moves with estimated positions.
• Invert a 1-2-3-4 triangular arrangement of pennies using minimum moves

  Answer: 3 moves
• Fill a 1-2-3-4 triangular arrangement of pennies with 9 pennies, leaving one cell empty. Pennies can jump over one penny to empty square, and the penny which is jumped over gets eliminated. Can you play the game so that finally one penny remains

  Answer: 

  
• Can you arrange 25 pennies on a surface, so that each penny touches exactly three other pennies?

  Answer: No. Count the total number of contact points with respect to each penny
• Can you arrange 24 pennies in such a manner?

  Answer: Yes, multiples of 4 are easy - take diamonds of 4 and arrange them back to back in a circle 

  

• You have three color paints - red, white and blue. You want to color every point in a plane using one of these colors. However, on any line in that plane, exactly two colors must appear.