The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Label this plum tree graph to make it totally magic!
An 8 by 8 chessboard is placed so that a black square is in the top left-hand corner. Starting in the top left square and working along each row in turn, coloured counters are placed, one on each square, following the sequence black, white, red, black, white, red, black, white, red and so on. When the right-hand end of each row is reached, the pattern continues, starting at the left-hand end
of the row beneath, until there is one counter on every square.
In the final arrangement, what fraction of the counters are on squares of the same colour as themselves?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.