# Live Problems - Stage 3, 4 & 5

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

The last day for sending in solutions to our live problems is Monday 17 May.

### Dozenslive

##### Age 7 to 14Challenge Level

Can you select the missing digit(s) to find the largest multiple?

### Clock Arithmeticlive

##### Age 11 to 18Challenge Level

What happens if we change the rules and make the usual straight number line into a circle?

### Starslive

##### Age 11 to 14Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

### More Adventures with Modular Arithmeticlive

##### Age 14 to 18Challenge Level

Investigate what happens when we add or multiply numbers using modular arithmetic.

### Clock Squareslive

##### Age 14 to 18Challenge Level

Can you find a way of predicting the value of large square numbers with the help of our power modulo calculator?

### Euler's Totient Functionlive

##### Age 16 to 18Challenge Level

How many numbers are there less than $n$ which have no common factors with $n$?

### Secondary Toughnutslive

##### Age 11 to 18Challenge Level

These secondary problems have not yet been solved. Can you be the first?