### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### F'arc'tion

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

### Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening? # The Greedy Algorithm ##### Stage: 3 Challenge Level: Rosie discusses this problem: The Greedy Algorithm always works, because there will always be a biggest unit fraction less than the one being dealt with, until you reach a unit fraction. You can see this by looking at different examples. If you have$\frac{x}{y}$then keep dividing$y$by increasing whole numbers until the result is less than$x$, say$a$is the smallest whole number such that$\frac{y}{a}< x$. (If they are equal then$\frac{x}{y}$itself is just a multiple of a unit fraction). Then$\frac{x}{y}=\frac{1}{a}+\frac{xa-y}{ay}$. The same process can be used now on$\frac{xa-y}{ay}\$ and so on until the remainder is a unit fraction.

I used the dictionary to find out what an algorithm was. It said
"A finite set of unambiguous instructions performed in a set sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result. Algorithms are the basis for most computer programming."
This means that it is a set of instructions that you follow, that finish in a specific number of moves.
A Greedy Algorithm is a special kind of algorithm.
"A greedy algorithm is any algorithm that follows the problem solving tactic of making the locally optimal choice at each stage with the hope of finding the global optimum."
So you do the best possible thing at each stage, in the hope of finding the best combination overall.