Grades 11-12 Video Solutions 2025-2025_11-12

Video Transcription

Video Summary

In a 4x4 chessboard, 16 kangaroos each occupy one square, and they must jump to a neighboring square every turn without leaving the board. After 100 turns, the goal is to find the maximum number of empty squares. The problem introduces invariants, explaining how kangaroos starting on a black square will return to a black square after an even number of turns, and the same applies to kangaroos starting on white squares. To maintain coloring parity after 100 turns, at minimum, one black and one white square must be occupied. By strategically jumping, all remaining kangaroos can be gathered on these two squares, leaving 14 others empty. Thus, the largest number of possible empty squares is 14, option B.

Keywords

4x4 chessboard

kangaroo jumps

maximum empty squares

coloring parity

strategic jumping