Exploring and noticing

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?

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?

A sequence is generated using these rules. For which values of n is the nth term equal to n?

One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?