A math problem in grade two of junior high school In the plane rectangular coordinate system, the point whose abscissa and ordinate are integers is called integral point. The unit length of the coordinate axis is 1. The integral point P starts from the origin o, and its velocity is 1 unit length / s, and it only moves to the right or upward. Two integral points (0,1), (1,0) can be reached in one second, three integral points (0,2), (1,1), (2,0) can be reached in two seconds, and (0,3), (1,2), (2,2) can be reached in three seconds, 1) (3,0) four integral points (1) When p starts from O for 4 seconds, which punctuality can p reach? (2) How many seconds did P move when it reached (65,3)? (3) Write all the punctual points you can reach in 8 seconds

A math problem in grade two of junior high school In the plane rectangular coordinate system, the point whose abscissa and ordinate are integers is called integral point. The unit length of the coordinate axis is 1. The integral point P starts from the origin o, and its velocity is 1 unit length / s, and it only moves to the right or upward. Two integral points (0,1), (1,0) can be reached in one second, three integral points (0,2), (1,1), (2,0) can be reached in two seconds, and (0,3), (1,2), (2,2) can be reached in three seconds, 1) (3,0) four integral points (1) When p starts from O for 4 seconds, which punctuality can p reach? (2) How many seconds did P move when it reached (65,3)? (3) Write all the punctual points you can reach in 8 seconds

It is easy to know that the integral point coordinates (a, b) to reach in N seconds is a, B ≥ 0, a + B = n (1) because 4 = 0 + 4 = 1 + 3 = 2 + 2, so (0,4), (4,0), (1,3), (3,1), (2,2) (2) to reach (65,3) needs to move 65 + 3 = 68 seconds (3) the same as (1) method 8 = 0 + 8