Problems
Biscuit Decorations
Stage: 1 Challenge Level: 
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Seven Sticks
Stage: 1 Challenge Level:
Explore the triangles that can be made with seven sticks of the same length.
Fencing
Stage: 2 Challenge Level:
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Rail Network
Stage: 2 Challenge Level:
This drawing shows the train track joining the Train Yard to all the stations labelled from A to S. Find a way for a train to call at all the stations and return to the Train Yard.
Train Timetable
Stage: 2 Challenge Level:
Use the information to work out the timetable for the three trains travelling between City station and Farmland station.
Shunting Puzzle
Stage: 2 Challenge Level:
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Single Track
Stage: 2 Challenge Level:
What is the best way to shunt these carriages so that each train can continue its journey?
Weighty Problem
Stage: 3 Challenge Level:
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Alphabet Soup
Stage: 3 Challenge Level:
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
First Forward Into Logo 1
Stage: 2, 3 and 4 Challenge Level:
A Short introduction to using Logo. This is the first in a twelve part series.
LOGO Challenge 1 - Star Square
Stage: 2, 3 and 4 Challenge Level:
Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.
Lower Bound
Stage: 3 Challenge Level:
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Pinned Squares
Stage: 3 Challenge Level:
The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .
Pie Cuts
Stage: 3 Challenge Level:
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
Bang's Theorem
Stage: 4 Challenge Level:
If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
Plus Minus
Stage: 4 Challenge Level:
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Pericut
Stage: 4 and 5 Challenge Level:
Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?
Ab Surd Ity
Stage: 5 Challenge Level:
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
Roots and Coefficients
Stage: 5 Challenge Level:
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
Janusz Asked
Stage: 5 Challenge Level:
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
