Reasoning, convincing and proving

How many possible symmetrical necklaces can you find? How do you know you've found them all?

How could you estimate the number of pencils/pens in these pictures?

Use the differences to find the solution to this Sudoku.

This activity focuses on doubling multiples of five.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?

Can you work out the values of J, M and C in this sum?

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?

If it takes 852 digits to number all the pages of a book, what is the number of the last page?

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?