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By considering rotations and reflections to be equivalent, prove that there exists only one 3x3 magic square.

If every combination of the digits 1,2,3,4 was written down, what would be the sum of the numbers formed?

What does F

_{$n$+2}/F_{$n$}tend towards as $n$ increases?Can you work out what fraction of the diagram is shaded?

Find the width of the annulus

Find the area of the annulus.

Is the claim about the average contents of matches in a matchbox correct?

Prove that $x$ + 1/$x$ ≥ 2 for non-negative values of $x$.

What fraction of the class in total have brown eyes?

How many unique four unit cube arrangements are there?

Show how you would label two wooden cubes to display any date of the month.

Find the probability that the three white candles will be adjacent

Can you discover the dimensions of the room?

Can you work out the most efficient way to plant trees?

Using a metre stick how would you find the internal diameter of a large circular pipe?

Can you find the area of the circumscribed triangle?

How many ways can you climb ten steps?

How should the 2nd die be coloured so that there is an equal chance of getting two faces of the same colour?

Can you prove that the product of three consecutive integers, plus their mean, is always cube?

Show that two consecutive primes cannot have a sum that is double a prime.

Can you determine the 1000

^{th}term of the sequence?How far can you see from the top of the Eiffel tower?

Can you work out how many girls are at the disco?

Prove that the only number of non-overlapping squares you cannot split a unit square into are 2, 3, or 5 smaller squares.

How many edges does a dodecagon have?

How many squares can you draw on a grid measuring 4 dots by 4 dots?

If $S_n$ represents the sum of the first $n$ odd numbers, prove that $4S_n = S_{2n}$.

What is the least number which has no remainder when divided by any number from 1 to 10?

Prove that the two angles in the square are congruent.

Prove that $n$($n$ + 1)(2$n$ + 1) is divisible by six for all integer values, $n$.

Solve the equation

`a`!`b`! =`a`! +`b`!Can you work out the teacher's favourite mathematician?

How many ways can a darts player finish from 150 points?

Using the digits 1, 2, 3, 4, and 5 to form 5-digit numbers, how many are divisible by 12?

Which of the boys, 1 to 3, is most likely to guess the colour of his hat?

Can you determine the best way to construct a set of steps leading up to a platform?

Can you determine the weight of the glass in the door?

By concatenating all of the digits 1, 2, 3, 4, and 5 to form the ratio of two numbers, how many ways can you make one-half?

Find the perimeter of the hexagon.

From the clues can you work out how many lockers there are?

Can you find the height of the cone?

Find the radius of the circle inscribed inside the isosceles triangle.

Find the radius of the circle inscribed inside the right angled triangle.

Find the side length of the square inscribed inside the right angled triangle.

Can you show when the product of fractions is an integer?

Which is greater in value, the square root of two or the cube root of three?

How far above the ground do the two ladders cross?

Can you find the exact value of the letter product?

Find the probability of winning the card game

What are the dimensions of the shaded square inside the 3-4-5 right angle triangle?

What is the password to unlock all secrets?

Use the given information to find the height of the mountain.

Can you work out the missing weight?

Can you work out how old the teacher really is?

How many lines are required to construct the Mystic Rose?

By considering all the nets of a unit cube, which net has the greatest perimeter?

Prove that $x$

^{2}+ $x$ + 1 will never divide by 5.Can you work out which numbers are on the two discs?

If you had discs numbered 1 to 10, how would you separate the discs into the two bags such that no bag contains its double?

How many ways can paint a cube with two colours?

Can you crack the hacker website password?

Can you work out how many pens the girl bought and how much she paid for each one?

Can you find the height of the cone?

What is the minimum number of marks required to measure the lengths 1 to 12?

Find the sum of all 4-digit combinations taken from {1,2,3,4,5}

Finding primes that are one less than a square.

Can you prove that all primes greater than 2 can be written as the difference of two squares?

Can you prove that the square of all primes minus 1 are divisible by 24?

How many primes less than 100 can be written as the sum of two square numbers?

Prove that seven is the only prime number that is one less than a perfect cube.

Show that $a/b = c/d = (a - c)/(b - d)$.

What proportion of 3-digit numbers contain the digit one?

How would you arrange the numbers 1 to 16 in the grid, such that the product of the numbers in each quadrant is divisible by 16?

How many different routes can you find through a 4 × 4 grid?

Find the connection between the constructed length and the original rectangle.

Given the three concentric circles generated by the rectangle show that the area of the inner circle equals the ring generated by the outer circles

Find the smallest number, greater than 1, which has a remainder of 1 when divided by any of 2, 3, 4, 5, 6, or 7

Investigating the divisibility of adding a 2-digit number to its reverse.

How many times between 9 a.m. and 3 p.m. is the angle between the hour and minute hand 90

^{o}?In the given right angle triangle prove that the two marked angles are the same size

Investigate the special number machine that square roots and rounds off answers.

Finding the chance of making a rounding error.

Can you discover the connection between the input values produce the same output from two different machines?

What should the length of the straight section be on a running track be to meet IAAF requirements?

How many 3-digit numbers have two digits the same?

Explain why a number made up of the same digit can only be prime if the digit is one AND the number of digits is itself prime

Using one sand glass that measures 9 minutes and another that measures 13 minutes, how would you measure 30 minutes?

From the information given, how can the goal keeper achieve a 50% save rate?

Find the area of the lunes on the semi-circle

Find the area of the shaded cross.

Can you find the area of the shaded square inside the triangle?

For a given denominator, prove that there are always an even number of simple fractions

Find the vertical height of the slide

Find the area of the sloping square.

Can you determine the point where the pole snapped?

Can you decrypt the punchline?

Which fits better... a round plug in a square hole or a square plug in a round hole?

How many squares can you make from 240 unit tiles?

Given that [

`n`(`n`+1)(`n`+2)]^{2}= 3039162537*6, find the value of *Using rods of length 1, 2, 3, ... ,

`n`, can you construct a square?Find the smallest repunit that is divisible by 63.

Can you make the sum equal to 100?

Prove that the tangential distances PS and PT are always equal.

Prove that the sum of the given angles are 360 degrees.

Can you work out how many tiles fill the room?

Given two points, X and Y, find the area of triangle OXY

Prove that exterior angle of a triangle is equal to the sum of two opposite interior angles

How long will it take for the train to completely pass through the tunnel?

Find the minimum number of socks which must be taken from the drawers to be certain of finding five matching pairs.

Can you discover the secret of this misleading system?

Can you use a combination of logic and algebra to determine Goldilock's weight?

Can you discover what X represents?