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 |
52 | Factor This | Factors | Factor 1000000 into a x b (neither a multiple of 10) | Prime factor decomposition |
52 | Fossils | Factors | Pretty little investigation of numbers reducing to a 'fossil' upon multiplication of their digits | Factor, Multiple |
52, 110 | Hundred factorial | Factors, Powers | How many zeros does 100! have on the end ? | Factor, Multiple, Verify |
56 | Double Squares | Squares | A surprisingly simple trick to writing numbers as the sums of squares - a must-see ! | Integer, Square number, Method |
60 | Egyptian Fractions | Fractions | Good practice in adding and subtracting to solve a fresh problem | Denominator, Numerator, Unit fraction, Multiple, Remainder |
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 |
66 | 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 |
80 | Ratio Cut | Ratio, Proportion | A
simple transformation makes easy work of a rectangle division.
|
Area, Ratio, Height |
82 | 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 |
90 | Twenty Four | Powers and Roots | Use three 2s to make 24 etc | Calculate, Powers, Roots |
86, 90 | Pity Four Fours | Order of Operations | Just the old 'make all the numbers from 1 to 20, using exactly four 4s' problem - with 4! and sqrt4 = 2 as tools... plus all the answers! | Arithmetic, Number Facts |
96 | Nearly Squares | Extend mental methods | Using the fact that 19 x 21 = 202 - 12 | Calculate, Partition |
96 | Half Squares | Extend mental methods | Using the fact that 6.52 = 6 x 7 + 0.25 | Calculate |
100, 206, 260 | Mean Square | Mental methods | A Magic Square, using means | Averages |
100, 228 | Smart Weights | Mental methods, Mass | The most efficient choice of weights is based on binary, but tertiary is even smarter ! | Power, Expression |
100, 146 | Christmas Partridges | Triangle numbers, Mental methods | My True Love seems to deal with Triangle numbers... | Systematic, Verify, Arithmetic sequence, Tn |
100, 230 | Britain Rules The Weights? | Binary, Mental methods | Metric weights aren't quite as efficient as you would hope... | Power, Double, Sequence |
110, 35 | Millennium Dates Palindromes | Checking, Written methods | How many Palindromic Dates will there be in the next Millennium ? | Systematic, Verify |
110, 32 | That's A Bit Odd | Checking, Reasoning | A simple Logic puzzle, requiring an assumption and checking whether that leads to a contradiction or not | Verify, Check, Contradiction |