Week beginning June 4th – Year 3 to Year 6
Looking at the diagram you can tell that if the x coordinate of the bottom right point on a line is even, the arrows in the line go down and right, otherwise, they go up and left. The point (18,17) is on the line with bottom right point (18+17-1,1) = (34,1). Because 34 is even, the arrows go down and right, so the next point is (19,16).
There are 74 points visited before the route reaches the point (9,4). The number of points visited follows the triangle numbers.
Number of points visited up to (1,1): 1
Number of points visited up to (2,1): 3
Number of points visited up to (1,3): 6
Number of points visited up to (4,1): 10
Therefore the number of points visited up to (1,11) is 66.
It is worth noticing here that because 9+4=13 is odd, the line points towards the top left, so we are starting at (1,11).
Then, we need to visit 8 points on the diagonal before reaching (9,4), which are to (1,12), (2,11), (3,10), (4,9), (5,8), (6,7), (7,6)
and (8,5) before reaching (9,4).
This is a total of 66+8=74 points visited before (9,4).