Explaining, convincing and proving

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try to explain why this works.

We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can you discover what the five different types of coins are worth and how many of each we have saved?

A huge wheel is rolling past your window. What do you see?

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?

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?