Being resilient

Do you have enough information to work out the area of the shaded quadrilateral?

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

Can you find the volumes of the mathematical vessels?

Two cannons are fired at one another and the cannonballs collide... what can you deduce?

Frosty the Snowman is melting. Can you use your knowledge of differential equations to find out how his volume changes as he shrinks?

Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.

Can you justify this equation involving three angles?