How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
How many tours visit each vertex of a cube once and only once? How
many return to the starting point?
Given probabilities of taking paths in a graph from each node, use
matrix multiplication to find the probability of going from one
vertex to another in 2 stages, or 3, or 4 or even 100.
A problem that did not need high level mathematics just clear thinking and
a little trigonometry. Well done to the large number of you who achieved a
correct solution, including Barinder, Roy, Dan and Calum - to name a few.
Go to last month's problems to see more solutions.
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.