Follow the clues to find the mystery number.
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
(a) You have 4 red and 5 blue counters. How many ways can they
be placed on a 3 by 3 grid so that all the rows columns and
diagonals have an even number of red counters?
(b) It is now only required that all the rows and columns have
an even number of red counters. Are there any additional solutions?
Two solutions are considered the same if one can be transformed to
the other by rotating the square.