# Spring 2017, problem 34

### Comments

I worked this problem using a basic fundamental math. I got the solution of 200 squares that the sailor can travel on.

You must have counted wrong, because the maximum can be no more than 196 by the following argument:

Consider the parity of the coordinates of the squares in the path. Taking every second square, there is alternation between EE/OO and EO/OE, where E and O stand for even and odd. If there are 15 rows, only 7 have even parity, and similarly with columns, so there are only 49 squares with parity EE, and hence a maximal payh length of 196.

@Purin is wrong. You missed two parts of the question. 1) The sailor can't enter and exit a square in a straight line. You did that going from 37 to 38. 2) The sailor must end on the square that he started one. You have him starting in a corner and ending in the middle.

The highest I found in 176. http://nyccami.org/what-do-you-do-with-a-dizzy-sailor/

I got 172. A question I had as an extension was to figure out this problem for each size grid from 2x2 - 15x15. And...is there a pattern (or function) in the largest number of squares for each size grid. Solange