# Farewell to Jenny Piggott - January 2011, Stage 2&3

In the summer of 2010, Jenny Piggott retired as NRICH Director and we held a farewell event for her. Colleagues and friends joined us to work together on problems they had suggested. This month we are featuring some tasks that were inspired by the day.

## Problems

### Dotty Six

##### Stage: 1 and 2 Challenge Level:

Dotty Six is a simple dice game that you can adapt in many ways.

### Shaping It

##### Stage: 1 and 2 Challenge Level:

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

### Bryony's Triangle

##### Stage: 2 Challenge Level:

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

### Button-up Some More

##### Stage: 2 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

### Semi-regular Tessellations

##### Stage: 3 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Troublesome Dice

##### Stage: 3 Challenge Level:

When dice land edge-up, we usually roll again. But what if we didn't...?

### Odds and Evens

##### Stage: 3 Challenge Level:

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

### Perimeter Expressions

##### Stage: 3 Challenge Level:

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

### Which Solids Can We Make?

##### Stage: 3 Challenge Level:

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?