Batch 3 - Class 212 - Game of LAP

• (Dudeney - 334) On a reduced chessboard of 49 squares, St George wishes to kill the dragon. Can you show how, starting from the central square, he may visit once, and only once, every square of the board in a chain of chess knight moves, and end by capturing the dragon on his last move? There are many ways of doing it so find a pretty design!

• Solution: 

  

• Each person divides their grid into four regions of 16 contiguous cells each. One player's grid is not shown to the second player. An example is shown below

• Now the players take turn to ask clues by asking for region mix of a 4x4 cell. For example, in the above grid, a player may ask EF34, which refers to cells E3, E4, F3, F4. The answer to this question is one I, three III. 
• The player who can guess the entire region divide for the other player first wins.

• A monk climbs a mountain. He starts at 8AM and reaches the summit at noon. He spends the night on the summit. The next morning, he leaves the summit at 8AM and descends by the same route that he used the day before, reaching the bottom at noon. Prove that there is a time between 8AM and noon at which the monk was at exactly the same spot on the mountain on both days.
• Answer: Let the monk climb up whichever way he wants. At the instant he begins his descent the next morning, have another monk hike up traveling exactly as the first monk did the first day. At some point, the two monks will meet on the trail. That is the time and place we want!