Exploring and Noticing Structure - Upper Secondary

Road Maker

Stage: 4 and 5 Challenge Level: Challenge Level:1

Which of these roads will satisfy a Munchkin builder?

Odd One Out

Stage: 5 Short Challenge Level: Challenge Level:1

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Simply Graphs

Stage: 5 Challenge Level: Challenge Level:1

Look for the common features in these graphs. Which graphs belong together?

Polite Numbers

Stage: 5 Challenge Level: Challenge Level:1

A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?

Impossible Triangles?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these triangular jigsaws are impossible to finish?

Fix Me or Crush Me

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make matrices which will fix one lucky vector and crush another to zero?

Pattern Recognition

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

When does a pattern start to exhibit structure? Can you crack the code used by the computer?