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Are these games fair? How can you tell?

How good are you at finding the formula for a number pattern ?

Can you fit the tangram pieces into the outlines of the people?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you use the given image to say something about the sum of an infinite series?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Can you fill in the mixed up numbers in this dilution calculation?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Can you prove that triangles are right-angled when $a^2+b^2=c^2$?