Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
Tic Tac Toe
Stage: 3 Challenge Level:
The ideas in this problem have been expanded and made into another, more detailed investigation. See Marbles in a Box.
In the game of Tic Tac Toe (i.e. noughts and crosses) there are 8 distinct winning lines.
Investigate how many distinct winning lines there are in a game played on a 3 by 3 by 3 board, with 27 cells.
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.