Weekly Problem 28 - 2006

What can you say about the rectangles that form this L-shape?

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

The ladybird squad members have an average of 12 spots each. How many spots does the pine ladybird have?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

Can you find the lap times of the two cyclists travelling at constant speeds?

On which of the hare's laps will she first pass the tortoise?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Which set of numbers that add to 10 have the largest product?

Take turns to remove a bead from the string. Can you find a way to play so that you will always win?

A game that demands a logical approach using systematic working to deduce a winning strategy

What is the last digit in this calculation involving powers?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

What average speed should Ms Fanthorpe drive at to arrive at work on time?

Can you choose one number from each row and column in this grid to form the largest possibe product?

Can you create a Latin Square from multiples of a six digit number?

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Weekly Problem 31 - 2017

The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

Can you find the next time that the 29th of February will fall on a Monday?

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

In this feature, you can see how some children started each task. This isn't because we want to give away the solutions!

In this feature, you can see how some children started each task, but this isn't because we want to give away the solutions!

This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics.

This article, the second in the series, looks at some different types of games and the sort of mathematical thinking they can develop.

Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse. . . .

Not all of us a bursting with creative game ideas, but there are several ways to go about creating a game that will assist even the busiest and most reluctant game designer.

Moving from the particular to the general, then revisiting the particular in that light, and so generalising further.

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

Weekly Problem 26 - 2008

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?