# Farewell to Jenny Piggott - January 2011, All Stages

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

### Pairs of Numbers

##### Age 5 to 7 Challenge Level:

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

### Button-up

##### Age 5 to 7 Challenge Level:

My coat has three buttons. How many ways can you find to do up all the buttons?

### Dotty Six

##### Age 5 to 11 Challenge Level:

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

### Shaping It

##### Age 5 to 11 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

##### Age 7 to 11 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

##### Age 7 to 11 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

##### Age 11 to 14 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

##### Age 11 to 14 Challenge Level:

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

### Odds and Evens

##### Age 11 to 14 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

##### Age 11 to 14 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?

##### Age 11 to 14 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?

### Fit for Photocopying

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

Explore the relationships between different paper sizes.

### 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?

### Dicey Decisions

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

Can you devise a fair scoring system when dice land edge-up or corner-up?

### Archimedes Numerical Roots

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

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

### Ante Up

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

Use cunning to work out a strategy to win this game.