# Exploring and Noticing Structure - Upper Secondary

##### Stage: 4 and 5 Challenge Level:

Which of these roads will satisfy a Munchkin builder?

### Odd One Out

##### Stage: 5 Short Challenge Level:

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:

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

### Polite Numbers

##### Stage: 5 Challenge Level:

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:

Which of these triangular jigsaws are impossible to finish?

### Fix Me or Crush Me

##### Stage: 5 Challenge Level:

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

### Pattern Recognition

##### Stage: 5 Challenge Level:

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