Weekly Problem 39 - 2012

For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

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.

Felix, Matthew, Alice, Robert,Hayden, Jenna, Catherine, James, James, Nick,Kieran, Kayleigh, Bethany, Luke and Matthew, all from Cupernham School; Andrei of School 205, Sophia of Stamford High School and Matthew of Finley Middle School all sent in correct solutions.

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

A game for 2 people, or play online. Given a target number,say 23, and a range of numbers to choose from, say 1-5, players take it in turns to add to the running total to hit their target number.