3 out of 3
Can you see how to build a harmonic triangle? Can you work out the next two rows?
3 out of 3
If a sum invested gains 10% each year how long before it has doubled its value?
1 out of 3
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
2 out of 3
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
2 out of 3
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
2 out of 3
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
3 out of 3
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
1 out of 3
Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.
1 out of 3
Find all the solutions to the this equation.
1 out of 3
Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
