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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.


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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