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Olivia and Poppy from St Mary's School, and Yanqing from Lipson Community College all suggested that the smallest total they could find is 8 using the route: 1-2-1-1-1-1-1.

Eva who goes to Benenden School sent in the largest total and describes the route:

1 (right to) 2 (right to) 1 (right to) 2 (down to) 1 (left to) 3 (left to) 3 (left to) 2 (down to) 1 (down to) 2 (right to) 1 (up to) 1 (right to) 1 (down to) 3 (right to) 1 Total = 25

Eva also sent in a path that made 12:

1 (right to) 2 (down to) 3 (down to) 1 (right to) 1 (down to) 3 (right to) 1

Emma from Maryhill High School found a different route that also has a total of 12:

1-2-3-3-1-1-1

Children at New Earswick Primary School found some other solutions to make 12:

Alex found:

1(right to) 2 (down to) 3 (down to) 1 (down to) 1 (right to) 3 (right to) 1.
 
Ben found:
1 (down to) 2 (right to) 3 (right to) 3 (down to) 1 (right to) 1 (down to) 1.
 
Josh found:
1 (down to) 2 (right to) 3 (right to ) 3 (right to) 1 (down to) 1(down to) 1.
 

Perhaps one of the last two is the same as Emma's - but well descibed, Alex, Ben and Josh.