Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you beat the computer in the challenging strategy game?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you coach your rowing eight to win?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Choose a symbol to put into the number sentence.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .