# August 2003, All Stages

## Problems

### Transformations Tables

##### Stage: 2 Challenge Level:

These grids are filled according to some rules - can you complete them?

### Let Us Reflect

##### Stage: 2 Challenge Level:

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

### Transforming the Letters

##### Stage: 2 Challenge Level:

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

### Transformations on a Pegboard

##### Stage: 2 Challenge Level:

How would you move the bands on the pegboard to alter these shapes?

### Clocks

##### Stage: 2 Challenge Level:

These clocks have been reflected in a mirror. What times do they say?

### The Number Crunching Machine

##### Stage: 2 Challenge Level:

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

### Reflecting Squarely

##### Stage: 3 Challenge Level:

In how many ways can you fit all three pieces together to make shapes with line symmetry?

### Threesomes

##### Stage: 3 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

### Bow Tie

##### Stage: 3 Challenge Level:

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

### Just Repeat

##### Stage: 3 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

### Stringing it Out

##### Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.

### Old Versions of NRICH Problems

##### Stage: 3, 4 and 5 Challenge Level:

Original text of NRICH problems, as featured in Charlie and Alison's BCME session 2018.

### Rots and Refs

##### Stage: 5 Challenge Level:

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

### Complex Rotations

##### Stage: 5 Challenge Level:

Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?

### Reflect Again

##### Stage: 5 Challenge Level:

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.