Inequalities

problem
All-variables Sudoku

Age

11 to 18

Challenge level

The challenge is to find the values of the variables if you are to solve this Sudoku.
problem
Classical means

Age

16 to 18

Challenge level

Use the diagram to investigate the classical Pythagorean means.
problem
Exhaustion

Age

16 to 18

Challenge level

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
problem
Power up

Age

16 to 18

Challenge level

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x
problem
Comparing continued fractions

Age

16 to 18

Challenge level

Which of these continued fractions is bigger and why?
problem
Biggest enclosure

Age

14 to 16

Challenge level

Three fences of different lengths form three sides of an enclosure. What arrangement maximises the area?
problem
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
Integral sandwich

Age

16 to 18

Challenge level

Generalise this inequality involving integrals.
problem
'Tis whole

Age

14 to 18

Challenge level

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
problem
Almost total inequality

Age

14 to 16

Challenge level