Inequalities

problem

Plutarch's Boxes

Age

11 to 14

Challenge level

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
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

Rationals Between...

Age

14 to 16

Challenge level

What fractions can you find between the square roots of 65 and 67?
problem

Mediant Madness

Age

14 to 16

Challenge level

Kyle and his teacher disagree about his test score - who is right?
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

Near 10

Age

14 to 16

Challenge level

10 must remain within easy reach...
problem

Powerful Order

Age

14 to 16

Challenge level

Powers of numbers might look large, but which of these is the largest...
problem

Not Continued Fractions

Age

14 to 18

Challenge level

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
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

Shades of Fermat's Last Theorem

Age

16 to 18

Challenge level

The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n + x^n = (x+1)^n so what about other solutions for x an integer and n= 2, 3, 4 or 5?