## Secondary Live Problems

Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.

The last day for submitting solutions to these live problems is Monday 14 October.

### Take Three From Five

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

### Cuboid challenge

What's the largest volume of box you can make from a square of paper?

### Slick Summing

Watch the video to see how Charlie works out the sum. Can you adapt his method?

## Secondary Students' Solutions

Take a look at these recently solved problems.

### Have you got it?

### Wipeout

### M, M and M

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

### Charlie's delightful machine

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?