To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problem-and-solution Word document.
Examples Page Ref | Problem Title | Objectives Ref | Description | Key Words |
36 | Millennium Dates Palindromes | Checking, Written methods | How many Palindromic Dates will there be in this new Millennium ? | Systematic, Verify |
53 | Divide It | Divisibility, Factors etc | Nice challenge involving tests of divisibility | Division, Verify |
53 | Factor This | Factors | Factor 1000000 into a x b (neither a multiple of 10) | Prime factor decomposition |
53, 145 | Factor Squares | Prime Factors, Sequences | Does the sequence 6, 12, 24,... contain any square numbers? | Prime factor decomposition |
53, 55 | Hundred factorial | Factors, Powers | How many zeros does 100! have on the end ? | Factor, Multiple, Verify |
55 | Fossils | Factors | Pretty little investigation of numbers reducing to a 'fossil' upon multiplication of their digits | Factor, Multiple |
57 | Double Squares | Squares | A surprisingly simple trick to writing numbers as the sums of squares - a must-see ! | Integer, Square number, Method |
57, 67 | Non-Calc Square Roots | Fractions, Square Roots | Newton's cute method to find square roots, and using addition and division of fractions too ! | Division, Verify |
57, 115 | Huge Powers | Index Laws, Powers | How to compare the relative sizes of numbers as huge as 2^{800} and 3^{600 }? | Power, Index laws |
59, 105 | Large Perfect Squares | Algebraic expressions, Refine written methods | This is based on the idea of squaring a bracket and the first few problems would be a nice 'long' multiplication revision puzzle | Partition, Multiply out, Square, Verify |
65 | Ordering Fractions | Fractions | This is a problem concerned with different ways to compare the size of fractions, and looking at alternative approaches, perhaps using approximations, differences or reciprocals. | Reciprocal, Equivalent, Estimate |
65, 67, 83 | That Fraction In Between | Fractions | Most students have tried the ' add the tops, then add the bottoms ' approach to adding fractions ... so this problem nicely explores the difference that this makes. | Equivalent, Estimate, Ascending |
65, 83 | What Was The Fraction? | Fractions, Reciprocals, Checking | Working back from a calculator display to the original fraction, using various techniques | Reciprocal, Equivalent, Division, Verify |
66 | Adding Fractions | Fractions | A series of fractions with horribly large denominators that can be simplified by intelligent grouping ...to give 1! | Sum, Factor, Denominator |
67 | Egyptian Fractions | Fractions | Good practice in adding and subtracting to solve a fresh problem | Denominator, Numerator, Unit fraction, Multiple, Remainder |
70, 150 | Christmas Partridges | Triangle numbers | My True Love seems to deal with Triangle numbers... | Systematic, Verify, Arithmetic sequence, T_{n} |
67 | Spare A Sheep | Finding and adding Fractions | Old Macdonald tries to share out his 19 sheep with the aid of a neighbour's sheep… | Fraction, Denominator |
77, 111 | Percentage Changes | Percentages, Checking | What % increase will compensate for a 5% decrease ? | Reciprocal, Inverse |
77 | The Property Market | Percentage changes | I sell two houses for £156000 - one at a 20% profit, the other at a 20% loss - am I winning or losing ? | _{Inverse, Profit, Loss} |
79, 81 | Astronomically Accurate | Proportion | _{How long is a year exactly (taking into account leap years and that)... and what about a real 'lunar' month?} | _{Proportion, Unitary, Accuracy} |
81 | Ratio Cut | Ratio, Proportion | A simple transformation makes easy work of a rectangle division. | Area, Ratio, Height |
81, 173 | Leg It | Interpret Graphs | _{Two runners are racing over 100m - how much start (or handicap) is needed to make the race a 'fair' one?} | _{Distance, Time, Speed, Ratio} |
81, 173 | Lap Times | Interpret Graphs | Two friends are running round a track at different speeds - how often do they pass each other? | Graphs, Ratio, Distance, Time |
81, 239 | What Size Are The Cylinders? | Ratio, Volume | Two similar cylinders come from a block of material - how big is each? | Ratio, Enlargement, Volume, Scale |
83 | Parking Meters | Use of Division, Sequences | A mixture of dollars and quarters make up $29.50 - how many coins of each type, 43 in total? | Calculate, Sequence |
87, 115 | Brackets | Order of operations, Brackets | The difference that the placing of brackets makes ! | Brackets, Associative, Commutative |
91, 101 | Pity Four Fours | Use known Number facts |
Just the old 'make all the numbers from 1 to 20, using exactly four 4s' problem - with 4! and Sq Rt (4) = 2 tools... plus all the answers! |
Arithmetic, Number Facts |
97 | Nearly Squares | Extend mental methods | Using the fact that 19 x 21 = 20^{2} - 1^{2} | Calculate, Partition |
97 | Half Squares | Extend mental methods | Using the fact that 6.5^{2} = 6 x 7 + 0.25 | Calculate |
100, 228 | Smart Weights | Mental methods, Mass | The most efficient choice of weights is based on binary, but tertiary is even smarter ! | Power, Expression |