# Posing Questions and Making Conjectures - Upper Secondary

### White Box

##### Age 7 to 18 Challenge Level:

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

### Pair Products

##### Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

### Difference Dynamics

##### Age 14 to 18 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

### Painting by Numbers

##### Age 16 to 18 Challenge Level:

How many different colours of paint would be needed to paint these pictures by numbers?

### Impossible Triangles?

##### Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

### The Clue Is in the Question

##### Age 16 to 18 Challenge Level:

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

### Supercomputer

##### Age 14 to 16 Short Challenge Level:

Weekly Problem 28 - 2014
What is the units digit of the given expression?

### Producing an Integer

##### Age 14 to 16 Short Challenge Level:

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

### Little Difference

##### Age 14 to 16 Short Challenge Level:

What is the value of $2006 \times 2008 - 2007 \times 2007$?

### Eulerian

##### Age 14 to 16 Short Challenge Level:

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?