Being resourceful

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

What is special about the difference between squares of numbers adjacent to multiples of three?

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Can you explain what is going on in these puzzling number tricks?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Can you create a Latin Square from multiples of a six digit number?

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?