Inequalities

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?

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

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

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

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

10 must remain within easy reach...

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

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

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?

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?