Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some
Stage: 5 Challenge Level:
A group of children are in a field and no two pairs of children are
at the same distance apart. Each child has a water pistol and
shoots the child nearest to them.
For different numbers of children, can you construct configurations
in which $0, 1, 2, 3, \cdots$ children get wet? Can you construct
configurations in which $0, 1, 2, 3, \cdots$ children stay dry? Is
there a largest or smallest number who could get wet in each case?
Do any patterns emerge?
It is a hot day and all of the children want to get wet? Can you
place them so that this is possible. Prove your results
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.