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 the 1st February.

Dozenslive

Age 7 to 14
Challenge Level

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

Take Three from Fivelive

Age 11 to 16
Challenge Level

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

Number Rules - OKlive

Age 14 to 16
Challenge Level

Can you produce convincing arguments that a selection of statements about numbers are true?

Always Perfectlive

Age 14 to 18
Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Common Divisorlive

Age 16 to 18
Challenge Level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

Polite Numberslive

Age 16 to 18
Challenge Level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

Digital Equationlive

Age 16 to 18
Challenge Level

Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?

Secondary Toughnutslive

Age 11 to 18
Challenge Level

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