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.
Can you guess the colours of the 10 marbles in the bag? Can you
develop an effective strategy for reaching 1000 points in the least
number of rounds?
Can you coach your rowing eight to win?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
Can you beat the computer in the challenging strategy game?
The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you make a 3x3 cube with these shapes made from small cubes?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
A cinema has 100 seats. Show how it is possible to sell exactly 100
tickets and take exactly £100 if the prices are £10 for
adults, 50p for pensioners and 10p for children.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
If these balls are put on a line with each ball touching the one in
front and the one behind, which arrangement makes the shortest line
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
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?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
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?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Using only six straight cuts, find a way to make as many pieces of
pizza as possible. (The pieces can be different sizes and shapes).
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
56 406 is the product of two consecutive numbers. What are these
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Factor track is not a race but a game of skill. The idea is to go
round the track in as few moves as possible, keeping to the rules.
Can you use the information to find out which cards I have used?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.