You can trace over all of the diagonals of a pentagon without
lifting your pencil and without going over any more than once. Can
the same thing be done with a hexagon or with a heptagon?
Stage: 2 Challenge Level:
You have 4 even numbers and 5 odd numbers and all the totals are odd. Think of the red counters as even numbers and the blues as odds. If diagonals can have any total then all three configurations give equivalent solutions because one can be transformed into another by interchanging rows or interchanging columns. If diagonals also have prime totals then only configuration (a) is possible
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. More information on many of our other activities
can be found here.