Inequalities

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

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Which of these continued fractions is bigger and why?

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

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.

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

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

Use the diagram to investigate the classical Pythagorean means.