Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
Age 14 to 16 Challenge Level
Two cubes, each with integral side lengths, have a combined
volume equal to the total of the lengths of their edges. How big
are the cubes? [If you find a result by 'trial and error' you'll
need to prove you have found all possible solutions.]
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.