Exploring and noticing

problem
Only connect

Age

11 to 14

Challenge level

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?
problem
Royal arm wrestling

Age

11 to 14

Challenge level

How many arm-wrestles will there be in the royal arm wrestling championship?
problem
Mobile numbers

Age

5 to 11

Challenge level

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
problem
Suit sequence

Age

11 to 14

Challenge level

A pattern repeats every six symbols. What are the 100th and 101st symbols?
problem
Who's who?

Age

11 to 16

Challenge level

Can you solve the clues to find out who's who on the friendship graph?
problem
12345

Age

14 to 16

Challenge level

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?
problem
Path to the stars

Age

7 to 11

Challenge level

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
problem
Arrange the digits

Age

11 to 14

Challenge level

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
problem
Out of sync

Age

11 to 14

Challenge level

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?
problem
Day of the Triffids

Age

14 to 16

Challenge level

Jasmine buys three different types of plant. How many triffids did she buy?