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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 mustsee !  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 = 20^{2}  1^{2}  Calculate, Partition 
96  Half Squares  Extend mental methods  Using the fact that 6.5^{2} = 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, T_{n} 
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 