Reasoning, convincing and proving

Here the diagram says it all. Can you find the diagram?

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

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

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

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

Nine cross country runners compete in a team competition in which there are three matches. If you were a judge how would you decide who would win?

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.