mathschallenge.net

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?