Image
Epsilons will be good for filling spare mathematical moments. Why not carry a few around with you?
problem
Purr-fection
Age
16 to 18
Challenge level
What is the smallest perfect square that ends with the four digits
9009?
problem
Real(ly) numbers
Age
16 to 18
Challenge level
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz
+ zx = 3. What is the largest value that any of the numbers can
have?
problem
Cut cube
Age
16 to 18
Challenge level
Find the shape and symmetries of the two pieces of this cut cube.
problem
Be reasonable
Age
16 to 18
Challenge level
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
progression.
problem
Shape and territory
Age
16 to 18
Challenge level
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
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?