# The Flying Colours Maths Blog: Latest posts

## A Puzzle From The MathsJam Shout (With Generating Functions)

In a recent MathsJam Shout, courtesy of Bristol MathsJam, we were given a situation, which I paraphrase: Cards bearing the letters A to E are shuffled and placed face-down on the table. You predict which of the cards bears which letter (You make all of your guesses before anything is

## Ask Uncle Colin: Solving Trigonometric Equations

Dear Uncle Colin, I’m trying to solve $2\cos(3x) = -\sqrt{2}$, for $0 \leq x \lt 2\pi$, but the answers I find are outside the specified interval, and obviously I miss the ones that are in the interval. How would you tackle this? - Like A Puzzle, Like A Cosine Equation

## Dictionary of Mathematical Eponymy: The Collatz Conjecture

What it is Every so often, one comes across a teacher who is Properly Evil. I’ll spare names here, but I have a clear, strong memory of being introduced to the Collatz conjecture on a school trip. “Take a number, let’s say 3. If it’s odd, you treble it and

## Ask Uncle Colin: Scheduling a tournament

Dear Uncle Colin, I’m trying to organise a tournament involving seven teams and two pitches. The following conditions must hold: Each team plays four games No pair of teams meets more than once Each team must play at most one pair of back-to-back matches How would you solve this? Bit

## The Mathematical Ninja and the Other Rope

This is based on a puzzle I heard from @colinthemathmo, who wrote it up here; he heard it from @DavidB52s, and there the trail goes cold. The Mathematical Ninja lay awake, toes itching. This generally meant that a mission was in the offing. Awake or dreaming? Unclear. But the thought