Exploring and noticing

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?

A pattern repeats every six symbols. What are the 100th and 101st symbols?

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

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?

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?

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

How do scores on dice and factors of polynomials relate to each other?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?