Inequalities

problem

Two Cubes

Age

14 to 16

Challenge level

2 out of 3

Two cubes have a combined volume equal to the total of the lengths of their edges. How big are the cubes?
problem

Rationals Between...

Age

14 to 16

Challenge level

2 out of 3

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

Mediant Madness

Age

14 to 16

Challenge level

2 out of 3

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

Biggest Enclosure

Age

14 to 16

Challenge level

2 out of 3

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

2 out of 3

10 must remain within easy reach...
problem

Powerful Order

Age

14 to 16

Challenge level

2 out of 3

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

Square Mean

Age

14 to 16

Challenge level

3 out of 3

Is the mean of the squares of two numbers greater than, or less than, the square of their means?
problem

Not Continued Fractions

Age

14 to 18

Challenge level

1 out of 3

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

2 out of 3

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

1 out of 3

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?