SEAMC published shorts

problem

Square within a square within...

Age

11 to 14

Challenge level

What fraction of this square is shaded?

problem

Rotation identification

Age

11 to 14

Challenge level

Which of these can be obtained by rotating this shape?

problem

Overlapping beer mats

Age

11 to 14

Challenge level

Can you find the area of the overlap when these two beer mats are placed on top of each other?

problem

Identical digit multiplication

Age

11 to 14

Challenge level

77 is multiplied by another two-digit number with identical digits. What is the product?

problem

Divisible digits

Age

11 to 14

Challenge level

Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

problem

Multiplication cube

Age

11 to 14

Challenge level

The net shown is folded up to form a cube. What is the largest possible vertex product?

problem

2014 even numbers

Age

11 to 14

Challenge level

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

problem

Nested squares

Age

11 to 14

Challenge level

What proportion of the diagram is shaded?

problem

Sum and differences

Age

11 to 14

Challenge level

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?

problem

Cuboid faces

Age

11 to 14

Challenge level

Can you find the volume of a cuboid, given the areas of its faces?

problem

Choose the mean

Age

11 to 14

Challenge level

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

problem

Fraction of a square

Age

11 to 14

Challenge level

What fraction of this square is shaded?

problem

Reverse ages

Age

11 to 14

Challenge level

When is the next time that Brian's age will be the reverse of his father's age?

problem

Draining a pool

Age

11 to 14

Challenge level

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

problem

Adding and multiplying

Age

11 to 14

Challenge level

Amy misread a question and got an incorrect answer. What should the answer have be?

problem

Bouncing ball

Age

11 to 14

Challenge level

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.

problem

Split clock face

Age

11 to 14

Challenge level

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.

problem

Strange dice

Age

11 to 14

Challenge level

If two of these unusually numbered dice are thrown, how many different sums are possible?

problem

Giant Rubik's cube

Age

11 to 14

Challenge level

How many cubes would be visible in a 12 by 12 by 12 Rubik's cube?

problem

Range of averages

Age

11 to 14

Challenge level

Find these 4 numbers, given their mode, median and range.

problem

Brothers and sisters

Age

11 to 14

Challenge level

Can you work out how many brothers and sisters are in the family?

problem

Missing digits

Age

11 to 14

Challenge level

Can you find the missing digits in this calculation?

problem

Speed over a bridge

Age

11 to 14

Challenge level

How fast is the train travelling as it goes over the bridge?

problem

Rough rectangle

Age

11 to 14

Challenge level

What is the smallest possible area that this rectangle could have?

problem

Hot dogs

Age

11 to 14

Challenge level

How many hot dogs did this hot dog lover eat on the first day of her binge?

problem

Shifting average

Age

11 to 14

Challenge level

What happens to the average if you subtract 8 from all of the numbers?

problem

Tile border

Age

11 to 14

Challenge level

What is the largest possible number of yellow tiles in this pattern?

problem

Dividing a square

Age

11 to 14

Challenge level

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

problem

Square grid

Age

11 to 14

Challenge level

Can you work out what fraction of this grid is shaded?

problem

Tilted tank

Age

11 to 14

Challenge level

Can you find the height of the water in this tilted tank when it is flat?

problem

The average age

Age

11 to 14

Challenge level

Given this information about averages, find the ages of these teachers.

problem

Multiplication mistake

Age

11 to 14

Challenge level

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

problem

Missing 9s

Age

11 to 14

Challenge level

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

problem

Product of fractions

Age

11 to 14

Challenge level

Find the product of these mixed numbers

problem

Red card blue card

Age

11 to 14

Challenge level

Can you arrange the red and blue cards so that the rules are all followed?

problem

Roses and carnations

Age

11 to 14

Challenge level

How many different bunches of flowers can this class buy for their teacher?

problem

Adding in pairs

Age

11 to 14

Challenge level

These are the results when 3 numbers were added in pairs. What were the numbers?

problem

Clubs

Age

11 to 14

Challenge level

How many students are in the maths club and the science club?

problem

The elephant diet

Age

11 to 14

Challenge level

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

problem

Linear area

Age

11 to 14

Challenge level

Find the area of the triangle enclosed by these lines.

problem

Lattice points on a line

Age

11 to 14

Challenge level

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

problem

French test

Age

11 to 14

Challenge level

What was the average score in this French test?

problem

Tiled floor

Age

11 to 14

Challenge level

This tiled floor has 109 purple tiles. How many tiles are there altogether?

problem

Scalene area

Age

11 to 14

Challenge level

Can you find the area of this scalene triangle?

problem

Diagonal side

Age

11 to 14

Challenge level

Can you work out the area of a square drawn on a diagonal?

problem

Smallest fraction

Age

11 to 14

Challenge level

Which of these is the smallest?

problem

Average temperature

Age

11 to 14

Challenge level

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

problem

Graph area

Age

11 to 14

Challenge level

Can you find the area between this graph and the x-axis, between x=3 and x=7?

problem

Charlie's money

Age

11 to 14

Challenge level

How much money did Charlie have to begin with?

problem

Between a sixth and a twelfth

Age

11 to 14

Challenge level

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

problem

Packing small boxes

Age

11 to 14

Challenge level

How many small boxes will fit inside the big box?

problem

Palindromic milometer

Age

11 to 14

Challenge level

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

problem

Last digit

Age

11 to 14

Challenge level

What is the last digit in this calculation involving powers?

problem

Washing elephants

Age

11 to 14

Challenge level

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

Use this series of fractions to find the value of x.

problem

Divisible by 55

Age

11 to 14

Challenge level

Choose the digits $a$ and $b$ so that this number is divisible by 55.

problem

Rain

Age

11 to 14

Challenge level

How many dry days did Aisha have on her holiday?

problem

Committees

Age

11 to 14

Challenge level

Every member of the club is a member of two committees. How many members are there in the club?

problem

Sum of 1s

Age

11 to 14

Challenge level

Can you find the last 5 digits of this sum?

problem

How shady?

Age

11 to 14

Challenge level

What fraction of this triangle is shaded?

problem

Black and gold storeys

Age

11 to 14

Challenge level

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

problem

Leap monday

Age

11 to 14

Challenge level

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

problem

Clock angle

Age

11 to 14

Challenge level

What is the angle between the the hands of a clock at 8:24?

problem

Number of arms

Age

11 to 14

Challenge level

What is the probability that the next person you meet has an above average number of arms?

problem

Add all the angles

Age

11 to 14

Challenge level

Find the sum of all of the angles denoted by letters in this diagram

problem

Cat on a wall

Age

14 to 16

Challenge level

How high is the wall that this cat is lying on?

problem

Length, width and area

Age

14 to 16

Challenge level

The area of a rectangle is 225 square units. Find its width.

problem

Ratio of areas

Age

14 to 16

Challenge level

What is the ratio of the area of the hexagon to the area of the triangle?

problem

Root 2017

Age

14 to 16

Challenge level

Between which two whole numbers is $\sqrt{2017}$ $?$

problem

Bobbly perimeter

Age

14 to 16

Challenge level

Find the perimeter of this shape made of semicircles

problem

Mean balance

Age

14 to 16

Challenge level

Given information about the mean, can you work out the missing numbers?

problem

Megabytes and kilobytes

Age

14 to 16

Challenge level

How many bytes are there in one megabyte?

problem

Flipping coins

Age

14 to 16

Challenge level

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

problem

Which face?

Age

14 to 16

Challenge level

Which faces are opposite each other when this net is folded into a cube?

problem

Table total

Age

14 to 16

Challenge level

Can you find the sum of all of the numbers in the table?

problem

Swapping sweets

Age

14 to 16

Challenge level

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?

problem

The power of the sum

Age

14 to 16

Challenge level

What is this sum, expressed as a power of 2?

problem

Power up to 1000

Age

14 to 16

Challenge level

Find $x+y$, where $2^x\times5^y=1000$

problem

Stacked cubes

Age

14 to 16

Challenge level

What is the total surface area of this shape?

problem

Two in a million

Age

14 to 16

Challenge level

What is the highest power of 2 that divides exactly into 1000000?

problem

Traffic tunnel

Age

14 to 16

Challenge level

Will these vehicles fit through this tunnel?

problem

Powerful expressions

Age

14 to 16

Challenge level

Put these expressions in order, from smallest to largest.

problem

Snapped palm tree

Age

14 to 16

Challenge level

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

problem

Hexagon perimeter

Age

14 to 16

Challenge level

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

problem

Strike a chord

Age

14 to 16

Challenge level

Can you work out the radius of a circle from some information about a chord?

problem

CD collection

Age

14 to 16

Challenge level

How many different ways can I arrange the CDs in my collection?

problem

Rough root

Age

14 to 16

Challenge level

Which of these options is closest to this square root?

problem

XOXOXO

Age

14 to 16

Challenge level

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

problem

Clever calculation

Age

14 to 16

Challenge level

Find the shortcut to do this calculation quickly!

problem

Coal truck

Age

14 to 16

Challenge level

What percentage of the truck's final mass is coal?

problem

Black and white socks

Age

14 to 16

Challenge level

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

problem

Diagonal area

Age

14 to 16

Challenge level

A square has area 72 cm$^2$. Find the length of its diagonal.

problem

Similar perimeter

Age

14 to 16

Challenge level

What are the possible perimeters of the larger triangle?

problem

Three right angles

Age

14 to 16

Challenge level

Work your way through these right-angled triangles to find $x$.

problem

Doubly isosceles

Age

14 to 16

Challenge level

Find the missing distance in this diagram with two isosceles triangles

problem

Maximum mean

Age

14 to 16

Challenge level

What is the largest that the mean of these numbers could be?

problem

The power of x

Age

14 to 16

Challenge level

Find the value of $x$ in this equation, where it appears in powers.

problem

Winding vine

Age

14 to 16

Challenge level

A vine is growing up a pole. Can you find its length?

problem

Odd dice

Age

14 to 16

Challenge level

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

problem

Cube factors

Age

14 to 16

Challenge level

How many factors of $9^9$ are perfect cubes?

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SEAMC published shorts