Powers and roots
problem
Enriching experience
Age
14 to 16
Challenge level
Find the five distinct digits N, R, I, C and H in the following
nomogram
problem
Pythagorean fibs
Age
16 to 18
Challenge level
What have Fibonacci numbers got to do with Pythagorean triples?
problem
Powerful order
Age
14 to 16
Challenge level
Powers of numbers might look large, but which of these is the largest...
problem
Rational roots
Age
16 to 18
Challenge level
Given that a, b and c are natural numbers show that if sqrt a+sqrt
b is rational then it is a natural number. Extend this to 3
variables.
problem
Plus or minus
Age
16 to 18
Challenge level
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
problem
Archimedes numerical roots
Age
16 to 18
Challenge level
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
Rationals between...
Age
14 to 16
Challenge level
What fractions can you find between the square roots of 65 and 67?
problem
Largest number
Age
11 to 14
Challenge level
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
problem
Irrational arithmagons
Age
16 to 18
Challenge level
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?