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# Exploring and Noticing Structure - Advanced

### Last Biscuit

### Vector Journeys

### Simply Graphs

### Root Hunter

### Spinners

### Impossible Triangles?

### Polite Numbers

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Age 11 to 18

Challenge Level

Can you find a strategy that ensures you get to take the last biscuit in this game?

Age 14 to 18

Challenge Level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Age 16 to 18

Challenge Level

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

Age 16 to 18

Challenge Level

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Age 16 to 18

Challenge Level

How do scores on dice and factors of polynomials relate to each other?

Age 16 to 18

Challenge Level

Which of these triangular jigsaws are impossible to finish?

Age 16 to 18

Challenge Level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?