# 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 these live problems is Monday 31 January.

### Three Neighbourslive

##### Age 7 to 14Challenge Level

Take three consecutive numbers and add them together. What do you notice?

### Three Consecutive Odd Numberslive

##### Age 11 to 16Challenge Level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

### Where Are the Primes?live

##### Age 11 to 16Challenge Level

What can we say about all the primes which are greater than 3?

##### Age 11 to 16Challenge Level

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

### Different Productslive

##### Age 14 to 16Challenge Level

Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

### What Does it All Add up To?live

##### Age 11 to 18Challenge Level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

### Impossible Sumslive

##### Age 14 to 18Challenge Level

Which numbers cannot be written as the sum of two or more consecutive numbers?

### Difference of Odd Squareslive

##### Age 14 to 18Challenge Level

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?

### Direct Logiclive

##### Age 16 to 18Challenge Level

Can you work through these direct proofs, using our interactive proof sorters?

### KS5 Proof Shortslive

##### Age 16 to 18Challenge Level

Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).

### Dodgy Proofslive

##### Age 16 to 18Challenge Level

These proofs are wrong. Can you see why?

### Secondary Toughnutslive

##### Age 11 to 18Challenge Level

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