Explaining, convincing and proving

The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?

Who is the youngest in this family?

How many bees could fly 1000 miles if they had 10 gallons of honey?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Jack does a 20-question quiz. How many questions didn't he attempt?

Fill in the grid with A-E like a Sudoku. Which letter is in the starred square?

Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?

Weekly Problem 21 - 2010
How many diagonals can you draw on this square...

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?