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How many pairs of positive integers add to make one-thousand?

Using positive integers, how many different sums add to make six?

Can you discover the password to unlock the tests?

Can you find the area of the arrow?

Show how to fill a ring with the digits 1 to 8 so that no two adjacent numbers are consecutive.

How many cuboids exist for which the volume is less than 100 units

^{3}and the integer side lengths are in an arithmetic sequence?Using the digits 1, 2, 3, and 4 (no more and no less), can you make all of the integers from 1 to 25?

Can you determine the set of five numbers given the average clues?

How many different weights can you weigh using 2 kg, 3 kg and 5 kg and a set of balancing scales?

Which corner will the beam of light emerge from the prism?

For how many 2-digit numbers is the first digit greater than the second digit?

Can you find out how many birds are in the cage?

Can you work out how many people attended the party?

The most efficient method of arranging songs on a tape.

How many children are standing in the circle?

Can you would out how much ten chocolate bars would cost?

Can you discover the minimum number of children in the class with brown hair and are right handed?

Using the information given, can you work out how many of each coin I have?

How many triangles are in a fully connected pentagon?

What is the maximum amount of money that you could have in your pocket and not able to make exactly £2?

How many nines are there in all of the numbers from 1 to 100?

How many squares are there altogether on a standard chessboard?

How many triangles are there in the diagram?

How many triangles are there in the diagram?

If all the counting numbers from 1 to 1000 were written out how many digits would be written down?

Can you discover how many miles from the station did the two trains cross?

From the information given, can you work out how many schools took part in the cross country race?

What question can you ask to ensure he gets to the Cuddly-Wuddly tribe?

What is the least number of Bishop pieces required to protect every square on a 8 by 8 chessboard?

What is the sum of the visible faces on the dice?

How long will the tortoise take to catch up with the hare?

By ensuring that the row and column in the grid have the same total, how many different totals can this be done with?

How many years during the twenty-first century has a square digital sum?

Investigating products of digits.

How many 3-digit numbers exist for which the sum of the digits is six?

How many numbers below one hundred are divisible by both 2 and 3?

Which numbers that are divisible by 10 can also be written as the sum of four consecutive integers?

How many Easter eggs will be bought by the family in total?

Which lengths, using one 2 m, two 3 m and one 8 m lenghts, can you measure directly?

Find the smallest multiple of nine containing only even digits.

What length of metal strips will be required to tile the roof of a 3x4 room?

Can you work out how old I am?

Can you discover the true weight of boy's sister?

Using four 4's (no more and no less), can you make all of the integers from 1 to 25?

What fraction of the square is shaded?

Can you work out the exact value of the fraction product?

Can you calculate how much would a passenger carrying 80 kg of luggage would be charged?

Can you find the palindrome using the clues?

How many cubes remain in the 5 × 5 × 5 cube?

Can you find the missing numerator and denominator to complete the fraction sum?

See if you can find the seed of this secret message.

How many white tiles will be needed to complete the kitchen floor design?

By adding a single unit square can you give the diagram a line of reflective symmetry?

What question can be used to logically deduce which address belongs to which parent?

Can you make 2 prime numbers using the digits 1, 2, 3 and 5?

Can you work out how far apart the trains were twenty minutes before passing each other?

How long will it take for two people to mow the lawn?

Can you discover how the number chain works?

How many 2-digit numbers have an odd product?

Can you work out who hit the centre target?

Can you work out which shape has the greatest perimeter?

On a 3x3x3 cube, how many cubes have exactly two faces painted?

Can you work out how fast Julie was travelling?

What is the largest gap between two consecutive palindromic years?

What is the minimum difference between two 5-digit pandigitals?

How many different ways can a 5x2 pathway be pathed with 2x1 paving stones?

How many peaceful queens can you place on a 4x4 chessboard?

A geometrical investigation using pentominoes.

What is the perimeter of the tenth pattern in the sequence?

Can you work out the minimum length of material required to make a frame for a photograph?

What is the biggest square based pyramid you can make from 1000 oranges?

How many ways can a £1 stamp book be filled with 9p first class and 7p second class stamps?

Investigating products that consist entirely of ones.

If you continue multiplying the digits in any 2-digit number, which starting numbers will finish on zero?

How many ways can exactly two quarter squares be shaded?

How many ways can you place a 3x2 block on a 4x3 grid?

Find the missing digit in the subtraction.

How many two digit primes can you find for which their reverse is also prime?

Explain why the hypotenuse is the longest side in a right angle triangle

How many years since the birth of Christ read the same upside-down?

Can you discover the meaning of the secret message written in the book?

What area of the squares are shaded?

How many different ways can a 2x2 grid be shaded?

By overlapping two equilateral triangles, find the area of the hexagaon

What fraction of the rectangle is shaded?

What fraction of the square is shaded?

By continuing the pattern, can you work out what fraction of a 20x20 grid will be shaded?

How many fractions with a denominator equal to 24 cannot be cancelled down?

Find the number of blocks needed to construct the 100th tower.

Can you work out when Augustus de Morgan was born?

Can you uncover the identity of the cult leader?

Without the use of any other measuring tools, how would you use a 2/3 m length of string to measure 1/2 m?

Find all 2-digit numbers that are equal to the sum of its digits product and sum

Find three different integers that add to sixteen, where the two smallest add to make the biggest.

Can you work out how much time will be saved by upgrading the computer system?

Creating diagrams using a traditional Chinese tangram.

How many matchsticks will be left if one-thousand houses are made?

Can you determine the lowest possible percentage score that the student scored in any one of the tests?

From the information, can you discover how old Sarah was when she retired?

Can you work out how many of the children are liars?

Can you split an equilateral triangle into six smaller triangles?

Can you discover the missing values in the triangular arithmagon?

Arranging triomino pieces of a 4×4 board.

Investigating the properties of the sum and product of digits.

Can you work out the combined weight of the boy, girl, and the dog?