Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Find the Fake
Age 14 to 16 Challenge Level:
There are 12 identical looking coins, one of which is a fake.
The counterfeit coin is of a different weight to the rest. Using
only a simple balance, what is the minimum number of weighings
needed to locate the fake coin and how is this done?
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.