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Add To One-thousand Problem ID: 136 (Dec 2003)
How many pairs of positive integers add to make one-thousand?
Add To Six Problem ID: 29 (Jan 2001)
Using positive integers, how many different sums add to make six?
Ancient Riddle Problem ID: 2 (Aug 2000)
Can you discover the password to unlock the tests?
Area Of Arrow Problem ID: 65 (Feb 2002)
Can you find the area of the arrow?
Arithmetic Ring Problem ID: 117 (May 2003)
Show how to fill a ring with the digits 1 to 8 so that no two adjacent numbers are consecutive.
Arithmetic Volume Problem ID: 198 (10 Jan 2005)
How many cuboids exist for which the volume is less than 100 units3 and the integer side lengths are in an arithmetic sequence?
As Easy As 1234 Problem ID: 13 (Sep 2000)
Using the digits 1, 2, 3, and 4 (no more and no less), can you make all of the integers from 1 to 25?
Average Problem Problem ID: 232 (31 Jul 2005)
Can you determine the set of five numbers given the average clues?
Balancing Scales Problem ID: 91 (Dec 2002)
How many different weights can you weigh using 2 kg, 3 kg and 5 kg and a set of balancing scales?
Beam Of Light Problem ID: 62 (Jan 2002)
Which corner will the beam of light emerge from the prism?
Bigger Digit Problem ID: 217 (30 Mar 2005)
For how many 2-digit numbers is the first digit greater than the second digit?
Birds And Bunnies Problem ID: 350 (17 Apr 2009)
Can you find out how many birds are in the cage?
Birthday Party Problem ID: 273 (21 Apr 2006)
Can you work out how many people attended the party?
CD To Tape Problem ID: 18 (Oct 2000)
The most efficient method of arranging songs on a tape.
Children In A Circle Problem ID: 30 (Jan 2001)
How many children are standing in the circle?
Chocolate Offer Problem ID: 122 (Oct 2003)
Can you would out how much ten chocolate bars would cost?
Class Distinction Problem ID: 192 (11 Dec 2004)
Can you discover the minimum number of children in the class with brown hair and are right handed?
Coin Problem Problem ID: 105 (Mar 2003)
Using the information given, can you work out how many of each coin I have?
Connected Pentagon Problem ID: 177 (Oct 2004)
How many triangles are in a fully connected pentagon?
Counting Coins Problem ID: 150 (Feb 2004)
What is the maximum amount of money that you could have in your pocket and not able to make exactly £2?
Counting Nines Problem ID: 100 (Feb 2003)
How many nines are there in all of the numbers from 1 to 100?
Counting Squares Problem ID: 107 (Mar 2003)
How many squares are there altogether on a standard chessboard?
Counting Triangles Problem ID: 42 (Apr 2001)
How many triangles are there in the diagram?
Counting Triangles Again Problem ID: 69 (Mar 2002)
How many triangles are there in the diagram?
Counting Up To One Thousand Problem ID: 323 (30 May 2007)
If all the counting numbers from 1 to 1000 were written out how many digits would be written down?
Crossing Trains Problem ID: 96 (Jan 2003)
Can you discover how many miles from the station did the two trains cross?
Cross Country Race Problem ID: 182 (01 Nov 2004)
From the information given, can you work out how many schools took part in the cross country race?
Cuddly Wuddly Tribe Problem ID: 335 (27 Mar 2008)
What question can you ask to ensure he gets to the Cuddly-Wuddly tribe?
Defensive Bishop Problem ID: 144 (Jan 2004)
What is the least number of Bishop pieces required to protect every square on a 8 by 8 chessboard?
Dice Problem Problem ID: 68 (Mar 2002)
What is the sum of the visible faces on the dice?
Different Speeds Problem ID: 225 (04 Jun 2005)
How long will the tortoise take to catch up with the hare?
Different Totals Problem ID: 85 (Nov 2002)
By ensuring that the row and column in the grid have the same total, how many different totals can this be done with?
Digital Square Sum Problem ID: 320 (14 Apr 2007)
How many years during the twenty-first century has a square digital sum?
Digit Product Problem ID: 17 (Oct 2000)
Investigating products of digits.
Digit Sum Problem ID: 206 (17 Feb 2005)
How many 3-digit numbers exist for which the sum of the digits is six?
Dividing 2 And 3 Problem ID: 45 (May 2001)
How many numbers below one hundred are divisible by both 2 and 3?
Divisible Consecutive Sums Problem ID: 33 (Feb 2001)
Which numbers that are divisible by 10 can also be written as the sum of four consecutive integers?
Easter Eggs Problem ID: 111 (Apr 2003)
How many Easter eggs will be bought by the family in total?
Efficient Measures Problem ID: 110 (Apr 2003)
Which lengths, using one 2 m, two 3 m and one 8 m lenghts, can you measure directly?
Even Digits Multiple Of Nine Problem ID: 327 (05 Jul 2007)
Find the smallest multiple of nine containing only even digits.
False Ceilings Problem ID: 59 (Dec 2001)
What length of metal strips will be required to tile the roof of a 3x4 room?
Father And Child Problem ID: 77 (May 2002)
Can you work out how old I am?
Faulty Scales Problem ID: 221 (24 May 2005)
Can you discover the true weight of boy's sister?
Four Fours Problem ID: 14 (Sep 2000)
Using four 4's (no more and no less), can you make all of the integers from 1 to 25?
Fraction Of A Square Problem ID: 46 (May 2001)
What fraction of the square is shaded?
Fraction Product Problem ID: 90 (Dec 2002)
Can you work out the exact value of the fraction product?
Heavy Baggage Problem ID: 116 (May 2003)
Can you calculate how much would a passenger carrying 80 kg of luggage would be charged?
Hidden Palindrome Problem ID: 163 (Apr 2004)
Can you find the palindrome using the clues?
Hollow Cube Problem ID: 27 (Dec 2000)
How many cubes remain in the 5 × 5 × 5 cube?
Incomplete Fractions Problem ID: 26 (Dec 2000)
Can you find the missing numerator and denominator to complete the fraction sum?
In The Beginning Problem ID: 5 (Aug 2000)
See if you can find the seed of this secret message.
Kitchen Floor Problem ID: 92 (Dec 2002)
How many white tiles will be needed to complete the kitchen floor design?
Lines Of Symmetry Problem ID: 38 (Mar 2001)
By adding a single unit square can you give the diagram a line of reflective symmetry?
Logically Addressed Question Problem ID: 258 (09 Jan 2006)
What question can be used to logically deduce which address belongs to which parent?
Making Primes Problem ID: 60 (Jan 2002)
Can you make 2 prime numbers using the digits 1, 2, 3 and 5?
Meeting Trains Problem ID: 261 (29 Jan 2006)
Can you work out how far apart the trains were twenty minutes before passing each other?
Mowing The Lawn Problem ID: 64 (Feb 2002)
How long will it take for two people to mow the lawn?
Number Chain Problem ID: 80 (Oct 2002)
Can you discover how the number chain works?
Odd Product Problem ID: 61 (Jan 2002)
How many 2-digit numbers have an odd product?
On Target Problem ID: 78 (May 2002)
Can you work out who hit the centre target?
Overlapping Rectangles Problem ID: 289 (22 Sep 2006)
Can you work out which shape has the greatest perimeter?
Painted Faces Problem ID: 129 (Nov 2003)
On a 3x3x3 cube, how many cubes have exactly two faces painted?
Palindromic Distance Problem ID: 267 (11 Feb 2006)
Can you work out how fast Julie was travelling?
Palindromic Years Problem ID: 143 (Jan 2004)
What is the largest gap between two consecutive palindromic years?
Pandigital Minimum Difference Problem ID: 202 (24 Jan 2005)
What is the minimum difference between two 5-digit pandigitals?
Pathed Pathways Problem ID: 57 (Dec 2001)
How many different ways can a 5x2 pathway be pathed with 2x1 paving stones?
Peaceful Queens Problem ID: 50 (Oct 2001)
How many peaceful queens can you place on a 4x4 chessboard?
Pentominoes Problem ID: 15 (Sep 2000)
A geometrical investigation using pentominoes.
Perimeter Sequence Problem ID: 76 (May 2002)
What is the perimeter of the tenth pattern in the sequence?
Picture Frame Problem ID: 308 (04 Feb 2007)
Can you work out the minimum length of material required to make a frame for a photograph?
Pile Of Oranges Problem ID: 34 (Feb 2001)
What is the biggest square based pyramid you can make from 1000 oranges?
Postage Stamps Problem ID: 58 (Dec 2001)
How many ways can a £1 stamp book be filled with 9p first class and 7p second class stamps?
Product Of Ones Problem ID: 23 (Nov 2000)
Investigating products that consist entirely of ones.
Product Of Zero Problem ID: 37 (Mar 2001)
If you continue multiplying the digits in any 2-digit number, which starting numbers will finish on zero?
Quarter Square Problem ID: 353 (23 Jul 2009)
How many ways can exactly two quarter squares be shaded?
Rectangular Arrangements Problem ID: 49 (Oct 2001)
How many ways can you place a 3x2 block on a 4x3 grid?
Reverse Difference Problem ID: 277 (13 May 2006)
Find the missing digit in the subtraction.
Reverse Prime Problem ID: 156 (Mar 2004)
How many two digit primes can you find for which their reverse is also prime?
Right Angle Reasoning Problem ID: 252 (12 Dec 2005)
Explain why the hypotenuse is the longest side in a right angle triangle
Rotational Years Problem ID: 41 (Apr 2001)
How many years since the birth of Christ read the same upside-down?
Seeing Clearly Problem ID: 8 (Aug 2000)
Can you discover the meaning of the secret message written in the book?
Shaded Area Problem ID: 22 (Nov 2000)
What area of the squares are shaded?
Shaded Grid Problem ID: 86 (Nov 2002)
How many different ways can a 2x2 grid be shaded?
Shaded Hexagon Problem ID: 149 (Feb 2004)
By overlapping two equilateral triangles, find the area of the hexagaon
Shaded Rectangle Problem ID: 106 (Mar 2003)
What fraction of the rectangle is shaded?
Shaded Square Problem ID: 228 (10 Jul 2005)
What fraction of the square is shaded?
Shading Pattern Problem ID: 101 (Feb 2003)
By continuing the pattern, can you work out what fraction of a 20x20 grid will be shaded?
Simple Fractions Problem ID: 72 (Apr 2002)
How many fractions with a denominator equal to 24 cannot be cancelled down?
Skeleton Towers Problem ID: 53 (Nov 2001)
Find the number of blocks needed to construct the 100th tower.
Square Age Problem ID: 31 (Jan 2001)
Can you work out when Augustus de Morgan was born?
Strawberry Milk Problem ID: 10 (Aug 2000)
Can you uncover the identity of the cult leader?
String Fractions Problem ID: 210 (06 Mar 2005)
Without the use of any other measuring tools, how would you use a 2/3 m length of string to measure 1/2 m?
Sum Digital Sum And Product Problem ID: 171 (May 2004)
Find all 2-digit numbers that are equal to the sum of its digits product and sum
Sum Of Three Problem ID: 25 (Dec 2000)
Find three different integers that add to sixteen, where the two smallest add to make the biggest.
System Upgrade Problem ID: 305 (20 Jan 2007)
Can you work out how much time will be saved by upgrading the computer system?
Tangrams Problem ID: 16 (Sep 2000)
Creating diagrams using a traditional Chinese tangram.
Terraced Houses Problem ID: 170 (May 2004)
How many matchsticks will be left if one-thousand houses are made?
Test Average Problem ID: 197 (21 Dec 2004)
Can you determine the lowest possible percentage score that the student scored in any one of the tests?
The Age Of Her Life Problem ID: 264 (05 Feb 2006)
From the information, can you discover how old Sarah was when she retired?
To Catch A Liar Problem ID: 255 (01 Jan 2006)
Can you work out how many of the children are liars?
Triangle Dissection Problem ID: 19 (Oct 2000)
Can you split an equilateral triangle into six smaller triangles?
Triangular Arithmetic Problem ID: 95 (Jan 2003)
Can you discover the missing values in the triangular arithmagon?
Triominoes Problem ID: 21 (Nov 2000)
Arranging triomino pieces of a 4×4 board.
Two-digit Sum And Product Problem ID: 118 (May 2003)
Investigating the properties of the sum and product of digits.
Weighing Scales Problem ID: 81 (Oct 2002)
Can you work out the combined weight of the boy, girl, and the dog?