Inequalities

problem
Favourite

In Between

Age

16 to 18

Challenge level

Can you find the solution to this algebraic inequality?
problem
Favourite

Discrete Trends

Age

16 to 18

Challenge level

Find the maximum value of n to the power 1/n and prove that it is a maximum.
problem
Favourite

Random Inequalities

Age

16 to 18

Challenge level

Can you build a distribution with the maximum theoretical spread?
problem

Two Cubes

Age

14 to 16

Challenge level

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]
problem

Reciprocals

Age

16 to 18

Challenge level

Prove that the product of the sum of n positive numbers with the sum of their reciprocals is not less than n^2.
problem

Classical Means

Age

16 to 18

Challenge level

Use the diagram to investigate the classical Pythagorean means.
problem

Comparing Continued Fractions

Age

16 to 18

Challenge level

Which of these continued fractions is bigger and why?
problem

Almost Total Inequality

Age

14 to 16

Challenge level
problem

Fracmax

Age

14 to 16

Challenge level

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
problem

Inequalities

Age

11 to 14

Challenge level

A bag contains 12 marbles. There are more red than green but green and blue together exceed the reds. The total of yellow and green marbles is more than the total of red and blue. How many of each colour there are in the bag?