List

SEAMC published shorts

Placeholder: several colourful numbers
problem

Sum and differences

Age
11 to 14
Challenge level
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Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?
Cuboid faces
problem

Cuboid faces

Age
11 to 14
Challenge level
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Can you find the volume of a cuboid, given the areas of its faces?
Choose the mean
problem

Choose the mean

Age
11 to 14
Challenge level
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Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
Reverse ages
problem

Reverse ages

Age
11 to 14
Challenge level
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When is the next time that Brian's age will be the reverse of his father's age?
Placeholder: several colourful numbers
problem

Draining a pool

Age
11 to 14
Challenge level
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The water is being drained from a pool. After how long will the depth of the pool be 144 cm?
Adding and multiplying
problem

Adding and multiplying

Age
11 to 14
Challenge level
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Amy misread a question and got an incorrect answer. What should the answer have be?
Bouncing ball
problem

Bouncing ball

Age
11 to 14
Challenge level
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A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.
Split clock face
problem

Split clock face

Age
11 to 14
Challenge level
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Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.
Placeholder: several colourful numbers
problem

Strange dice

Age
11 to 14
Challenge level
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If two of these unusually numbered dice are thrown, how many different sums are possible?
Giant Rubik's Cube
problem

Giant Rubik's cube

Age
11 to 14
Challenge level
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How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

Placeholder: several colourful numbers
problem

Range of averages

Age
11 to 14
Challenge level
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Find these 4 numbers, given their mode, median and range.
Brothers and sisters
problem

Brothers and sisters

Age
11 to 14
Challenge level
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Can you work out how many brothers and sisters are in the family?
Missing Digits
problem

Missing digits

Age
11 to 14
Challenge level
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Can you find the missing digits in this calculation?
speed over a bridge
problem

Speed over a bridge

Age
11 to 14
Challenge level
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How fast is the train travelling as it goes over the bridge?
Placeholder: several colourful numbers
problem

Rough rectangle

Age
11 to 14
Challenge level
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What is the smallest possible area that this rectangle could have?
Hot Dogs
problem

Hot dogs

Age
11 to 14
Challenge level
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How many hot dogs did this hot dog lover eat on the first day of her binge?
Placeholder: several colourful numbers
problem

Rotation identification

Age
11 to 14
Challenge level
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Which of these can be obtained by rotating this shape?
Overlapping beer mats
problem

Overlapping beer mats

Age
11 to 14
Challenge level
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Can you find the area of the overlap when these two beer mats are placed on top of each other?
Identical digit multiplication
problem

Identical digit multiplication

Age
11 to 14
Challenge level
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77 is multiplied by another two-digit number with identical digits. What is the product?
Divisible digits
problem

Divisible digits

Age
11 to 14
Challenge level
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Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
Placeholder: several colourful numbers
problem

Multiplication cube

Age
11 to 14
Challenge level
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The net shown is folded up to form a cube. What is the largest possible vertex product?
2014 even numbers
problem

2014 even numbers

Age
11 to 14
Challenge level
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What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
Placeholder: several colourful numbers
problem

Nested squares

Age
11 to 14
Challenge level
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What proportion of the diagram is shaded?
Missing 9s
problem

Missing 9s

Age
11 to 14
Challenge level
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Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?
Red card blue card
problem

Red card blue card

Age
11 to 14
Challenge level
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Can you arrange the red and blue cards so that the rules are all followed?
Placeholder: several colourful numbers
problem

Roses and carnations

Age
11 to 14
Challenge level
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How many different bunches of flowers can this class buy for their teacher?
Placeholder: several colourful numbers
problem

Adding in pairs

Age
11 to 14
Challenge level
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These are the results when 3 numbers were added in pairs. What were the numbers?
Placeholder: several colourful numbers
problem

Clubs

Age
11 to 14
Challenge level
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How many students are in the maths club and the science club?
Placeholder: several colourful numbers
problem

The elephant diet

Age
11 to 14
Challenge level
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Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
Placeholder: several colourful numbers
problem

Linear area

Age
11 to 14
Challenge level
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Find the area of the triangle enclosed by these lines.
Lattice points on a line
problem

Lattice points on a line

Age
11 to 14
Challenge level
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How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
Placeholder: several colourful numbers
problem

Tiled floor

Age
11 to 14
Challenge level
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This tiled floor has 109 purple tiles. How many tiles are there altogether?
Scalene area
problem

Scalene area

Age
11 to 14
Challenge level
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Can you find the area of this scalene triangle?
Placeholder: several colourful numbers
problem

French test

Age
11 to 14
Challenge level
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What was the average score in this French test?
Placeholder: several colourful numbers
problem

Diagonal side

Age
11 to 14
Challenge level
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Can you work out the area of a square drawn on a diagonal?
Placeholder: several colourful numbers
problem

Smallest fraction

Age
11 to 14
Challenge level
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Which of these is the smallest?
Placeholder: several colourful numbers
problem

Average temperature

Age
11 to 14
Challenge level
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The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?
Graph Area
problem

Graph area

Age
11 to 14
Challenge level
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Can you find the area between this graph and the x-axis, between x=3 and x=7?
Placeholder: several colourful numbers
problem

Between a sixth and a twelfth

Age
11 to 14
Challenge level
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The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
Placeholder: several colourful numbers
problem

Charlie's money

Age
11 to 14
Challenge level
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How much money did Charlie have to begin with?
Placeholder: several colourful numbers
problem

Packing small boxes

Age
11 to 14
Challenge level
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How many small boxes will fit inside the big box?
Palindromic milometer
problem

Palindromic milometer

Age
11 to 14
Challenge level
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At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?
Placeholder: several colourful numbers
problem

Shifting average

Age
11 to 14
Challenge level
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What happens to the average if you subtract 8 from all of the numbers?
Placeholder: several colourful numbers
problem

Tile border

Age
11 to 14
Challenge level
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What is the largest possible number of yellow tiles in this pattern?
Dividing a square
problem

Dividing a square

Age
11 to 14
Challenge level
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A square is divided into three shapes which all have equal areas. Can you find the length of this side?
Placeholder: several colourful numbers
problem

Square grid

Age
11 to 14
Challenge level
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Can you work out what fraction of this grid is shaded?
Tilted tank
problem

Tilted tank

Age
11 to 14
Challenge level
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Can you find the height of the water in this tilted tank when it is flat?
Placeholder: several colourful numbers
problem

The average age

Age
11 to 14
Challenge level
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Given this information about averages, find the ages of these teachers.
Multiplication Mistake
problem

Multiplication mistake

Age
11 to 14
Challenge level
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Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?
Placeholder: several colourful numbers
problem

Rain

Age
11 to 14
Challenge level
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How many dry days did Aisha have on her holiday?
Committees
problem

Committees

Age
11 to 14
Challenge level
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Every member of the club is a member of two committees. How many members are there in the club?
Sum of 1s
problem

Sum of 1s

Age
11 to 14
Challenge level
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Can you find the last 5 digits of this sum?
Placeholder: several colourful numbers
problem

How shady?

Age
11 to 14
Challenge level
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What fraction of this triangle is shaded?
Black and gold storeys
problem

Black and gold storeys

Age
11 to 14
Challenge level
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25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...
Leap Monday
problem

Leap monday

Age
11 to 14
Challenge level
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Can you find the next time that the 29th of February will fall on a Monday?
Clock angle
problem

Clock angle

Age
11 to 14
Challenge level
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What is the angle between the the hands of a clock at 8:24?
Placeholder: several colourful numbers
problem

Number of arms

Age
11 to 14
Challenge level
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What is the probability that the next person you meet has an above average number of arms?
Placeholder: several colourful numbers
problem

Add all the angles

Age
11 to 14
Challenge level
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Find the sum of all of the angles denoted by letters in this diagram
last digit
problem

Last digit

Age
11 to 14
Challenge level
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What is the last digit in this calculation involving powers?
Placeholder: several colourful numbers
problem

Washing elephants

Age
11 to 14
Challenge level
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How long will it take Mary and Nigel to wash an elephant if they work together?
tricky fractions
problem

Tricky fractions

Age
11 to 14
Challenge level
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Use this series of fractions to find the value of x.
Placeholder: several colourful numbers
problem

Divisible by 55

Age
11 to 14
Challenge level
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Choose the digits $a$ and $b$ so that this number is divisible by 55.
Mean balance
problem

Mean balance

Age
14 to 16
Challenge level
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Given information about the mean, can you work out the missing numbers?
Flipping coins
problem

Flipping coins

Age
14 to 16
Challenge level
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A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
Placeholder: several colourful numbers
problem

Which face?

Age
14 to 16
Challenge level
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Which faces are opposite each other when this net is folded into a cube?
Table Total
problem

Table total

Age
14 to 16
Challenge level
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Can you find the sum of all of the numbers in the table?
Swapping Sweets
problem

Swapping sweets

Age
14 to 16
Challenge level
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If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?
Placeholder: several colourful numbers
problem

Power up to 1000

Age
14 to 16
Challenge level
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Find $x+y$, where $2^x\times5^y=1000$
Placeholder: several colourful numbers
problem

The power of the sum

Age
14 to 16
Challenge level
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What is this sum, expressed as a power of 2?
Placeholder: several colourful numbers
problem

Stacked cubes

Age
14 to 16
Challenge level
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What is the total surface area of this shape?
Placeholder: several colourful numbers
problem

Cat on a wall

Age
14 to 16
Challenge level
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How high is the wall that this cat is lying on?
Placeholder: several colourful numbers
problem

Length, width and area

Age
14 to 16
Challenge level
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The area of a rectangle is 225 square units. Find its width.
Placeholder: several colourful numbers
problem

Ratio of areas

Age
14 to 16
Challenge level
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What is the ratio of the area of the hexagon to the area of the triangle?
Placeholder: several colourful numbers
problem

Root 2017

Age
14 to 16
Challenge level
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Between which two whole numbers is $\sqrt{2017}$ $?$
Bobbly perimeter
problem

Bobbly perimeter

Age
14 to 16
Challenge level
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Find the perimeter of this shape made of semicircles
Placeholder: several colourful numbers
problem

Similar perimeter

Age
14 to 16
Challenge level
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What are the possible perimeters of the larger triangle?
Placeholder: several colourful numbers
problem

Three right angles

Age
14 to 16
Challenge level
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Work your way through these right-angled triangles to find $x$.
Placeholder: several colourful numbers
problem

Doubly isosceles

Age
14 to 16
Challenge level
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Find the missing distance in this diagram with two isosceles triangles
Placeholder: several colourful numbers
problem

Maximum mean

Age
14 to 16
Challenge level
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What is the largest that the mean of these numbers could be?
Placeholder: several colourful numbers
problem

The power of x

Age
14 to 16
Challenge level
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Find the value of $x$ in this equation, where it appears in powers.

Winding vine
problem

Winding vine

Age
14 to 16
Challenge level
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A vine is growing up a pole. Can you find its length?
Placeholder: several colourful numbers
problem

Odd dice

Age
14 to 16
Challenge level
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These strange dice are rolled. What is the probability that the sum obtained is an odd number?
Placeholder: several colourful numbers
problem

Cube factors

Age
14 to 16
Challenge level
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How many factors of $9^9$ are perfect cubes?
Square to a rectangle
problem

Square to a rectangle

Age
14 to 16
Challenge level
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Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?
Placeholder: several colourful numbers
problem

Pineapple juice

Age
14 to 16
Challenge level
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What percentage of this orange drink is juice?
Placeholder: several colourful numbers
problem

Photocopied map

Age
14 to 16
Challenge level
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What will the scale on this map be after it has been photocopied?
Placeholder: several colourful numbers
problem

How many squares?

Age
14 to 16
Challenge level
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How many 4-digit numbers are perfect squares?
Semicircle distance
problem

Semicircle distance

Age
14 to 16
Challenge level
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Can you find the shortest distance between the semicircles given the area between them?
Placeholder: several colourful numbers
problem

Arc radius

Age
14 to 16
Challenge level
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Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?
Placeholder: several colourful numbers
problem

Rotation and area

Age
14 to 16
Challenge level
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Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?
Placeholder: several colourful numbers
problem

Root estimation

Age
14 to 16
Challenge level
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Which of these is the best approximation for this square root?
Placeholder: several colourful numbers
problem

Climbing ropes

Age
14 to 16
Challenge level
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Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?
Cones and spheres
problem

Cones and spheres

Age
14 to 16
Challenge level
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A solid metal cone is melted down and turned into spheres. How many spheres can be made?
Placeholder: several colourful numbers
problem

Thousands of x

Age
14 to 16
Challenge level
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Can you solve this scary-looking equation?