Question number 19. A new chess piece called Kangaroo has been introduced. In each move, it jumps either 3 squares vertically and 1 square horizontally, or 3 squares horizontally and 1 square vertically, as shown in the picture. What is the minimum number of moves the kangaroo needs to make in order to get from its current position to the square mark with A? Here is that diagram representing the kangaroo's possible moves. Let me make a larger copy of it. Here is the kangaroo again. His destination is 1 block over, marked with A. Each one of the moves in that general direction will overshoot the kangaroo's destination, so he has to double back. Let's imagine that he is already at his destination. What move is the best possible move for him to make one step prior to arriving at his destination? He is somewhere over here, after moving in the general direction of A, and then he is mysteriously making the last jump. I think if we were to follow back from A, we would have to go in reverse, trying to match the pointy end of one of these arrows with the tail of one of the other possible arrows. I think if we could copy one of these arrows down, we could see what's going on. Let's do that. Let's reverse the kangaroo's direction here. I'll outline one of these arrows here in red, and then move it back to represent the kangaroo's possible path. Here we go. If he were making one move in reverse from A, he would actually be here in this field. Let me put him where he needs to go. He would be here, and then moving towards A. Now, from that position, can we tell is there a move that would connect these arrows somehow? Can we connect these two arrows with one possible move? The answer is, well, no, because they're too close to one another, but perhaps we can fit an arrow in here. That looks like it would be maybe this arrow. I'll outline it in blue. Let's see if we can position it into the right squares. Like so. And then let me move that over. And will that work? It looks like it will work. The kangaroo would first make a jump along the black arrow over here, then along the blue arrow to where he is pictured, and then one more jump would take him to his destination at A. That requires a minimum of three moves, so that would be the answer to this problem. A minimum of three moves is required. That would be three.

chess

Kangaroo

movement

backtrack

strategy