2 out of 3
By proving these particular identities, prove the existence of general cases.
2 out of 3
Discover how networks can be used to prove Euler's Polyhedron formula.
2 out of 3
Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?
3 out of 3
Can the pdfs and cdfs of an exponential distribution intersect?
3 out of 3
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.
3 out of 3
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
3 out of 3
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
3 out of 3
We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
3 out of 3
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
3 out of 3
With n people anywhere in a field each shoots a water pistol at the nearest person. In general who gets wet? What difference does it make if n is odd or even?
