| 30 | Everyone shakes handsCounting | Easy | Lemma | Counting pairsAvoiding double counting | |
| 43 | Every subsetCounting | Easy | Lemma | Powers of twoIndependent choices | |
| 44 | Choosing a pairCounting | Easy | Lemma | Combinationsn choose 2 | |
| 603 | Four different digitsCounting | Easy | Lemma | Counting | |
| 604 | Licence platesCounting | Easy | Lemma | Counting | |
| 605 | Around a tableCounting | Easy | Lemma | Counting | |
| 606 | Anagrams of BANANACounting | Easy | Lemma | Counting | |
| 607 | President and vice-presidentCounting | Easy | Lemma | Counting | |
| 609 | Walking on a gridCounting | Easy | Lemma | Counting | |
| 610 | Diagonals of a decagonCounting | Easy | Lemma | Counting | |
| 800 | Arranging MISSISSIPPICounting | Easy | Lemma | Counting | |
| 848 | Consonant‑vowel selectionCounting | Easy | Hall & Knight | permutationscombinations | |
| 849 | Scholarship assignmentsCounting | Easy | Hall & Knight | product rule | |
| 850 | Arrangements of equationCounting | Easy | Hall & Knight | permutations | |
| 853 | Changes with five bellsCounting | Easy | Hall & Knight | permutations | |
| 854 | Changes with seven bells, tenor fixedCounting | Easy | Hall & Knight | permutations with restriction | |
| 856 | Council and Alderman CommitteeCounting | Easy | Hall & Knight | combinationsmultinomial | |
| 857 | Combinations of Fifty Choose Forty‑SixCounting | Easy | Hall & Knight | binomial coefficient | |
| 859 | Selecting a PartyCounting | Easy | Hall & Knight | combinationssubsets | |
| 865 | Allocating volunteers to districtsCounting | Easy | Hall & Knight | multinomialallocation | |
| 866 | Books on a shelf with English in middleCounting | Easy | Hall & Knight | selectionarrangement | |
| 868 | Shelving volumes of worksCounting | Easy | Hall & Knight | blocksinternal order | |
| 869 | Best and worst papers apartCounting | Easy | Hall & Knight | complementary counting | |
| 872 | Permutation ratio problemCounting | Easy | Hall & Knight | permutationsalgebraic manipulation | |
| 873 | Flag signal arrangementsCounting | Easy | Hall & Knight | permutationssum of series | |
| 874 | Binomial ratio problemCounting | Easy | Hall & Knight | binomial coefficientsalgebraic solving | |
| 879 | Choosing conveyances for three tripsCounting | Easy | Hall & Knight | independent choices | |
| 880 | Colourful counter arrangementsCounting | Easy | Hall & Knight | permutationsmultiset | |
| 881 | Loading animals onto stallsCounting | Easy | Hall & Knight | choicesexponentiation | |
| 882 | Distributing items to personsCounting | Easy | Hall & Knight | functionsassignments | |
| 883 | Dividing five objects between two peopleCounting | Easy | Hall & Knight | distributionexclusion | |
| 884 | Permutations of repeated lettersCounting | Easy | Hall & Knight | multinomialrepetition | |
| 885 | Unsuccessful letter‑lock attemptsCounting | Easy | Hall & Knight | product rulecomplement | |
| 886 | Triangles from a 15‑gonCounting | Easy | Hall & Knight | combinationsgeometric counting | |
| 888 | Numbers below 10000Counting | Easy | Hall & Knight | base‑8 countingenumeration | |
| 890 | Telegraph signalsCounting | Easy | Hall & Knight | exponential countingexclusion | |
| 891 | Drawing money from a bagCounting | Easy | Hall & Knight | subsetsbinary choices | |
| 894 | Flag signallingCounting | Easy | Hall & Knight | subsetspermutations | |
| 904 | Permutation 8P7Counting | Easy | Hall & Knight | permutations | |
| 905 | Permutation 25P5Counting | Easy | Hall & Knight | permutations | |
| 906 | Combination 24C4Counting | Easy | Hall & Knight | combinations | |
| 907 | Combination 19C14Counting | Easy | Hall & Knight | combinations | |
| 908 | Permutations of triangleCounting | Easy | Hall & Knight | permutations | |
| 909 | Permutations beginning with t and ending with eCounting | Easy | Hall & Knight | permutations | |
| 910 | Choosing four digitsCounting | Easy | Hall & Knight | combinationsselection | |
| 911 | Four‑digit numbersCounting | Easy | Hall & Knight | permutationsarrangements | |
| 912 | Choosing watches of four menCounting | Easy | Hall & Knight | combinations | |
| 913 | Watches containing a given manCounting | Easy | Hall & Knight | combinations | |
| 917 | Ring arrangements of seven peopleCounting | Easy | Hall & Knight | circular permutations | |
| 923 | Arrangements Starting with CapitalCounting | Easy | Hall & Knight | permutationsrestricted positions | |
| 924 | Arrangements Starting and Ending with CapitalCounting | Easy | Hall & Knight | permutationsrestricted positions | |
| 927 | Committee with Exactly One OfficerCounting | Easy | Hall & Knight | combinations | |
| 928 | Committee with At Least One OfficerCounting | Easy | Hall & Knight | combinations | |
| 1538 | Multinomial Coefficient 1Counting | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1539 | Multinomial Coefficient 2Counting | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1540 | Multinomial Coefficient 3Counting | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1542 | Trinomial Coefficient 1Counting | Easy | Hall & Knight | Multinomial TheoremPolynomial Expansion | |
| 53 | Corner to cornerCounting paths | Medium | Lemma | CombinationsArranging steps | |
| 54 | Balls into boxesCounting | Medium | Lemma | Stars and bars | |
| 608 | Sharing ten sweetsCounting | Medium | Lemma | Counting | |
| 851 | Finding n from permutation conditionCounting | Medium | Hall & Knight | permutationsequations | |
| 852 | Finding n from a ratio of combinationsCounting | Medium | Hall & Knight | binomial coefficientsequation solving | |
| 855 | Arrangements of draught with adjacent vowelsCounting | Medium | Hall & Knight | permutationsgrouping | |
| 858 | Arrangements with Odd‑Place LettersCounting | Medium | Hall & Knight | permutationsrestricted positions | |
| 861 | Words from Consonants and VowelsCounting | Medium | Hall & Knight | selectionarrangement | |
| 862 | Shelf Arrangement of BooksCounting | Medium | Hall & Knight | selectionordering | |
| 863 | Equal Division of ObjectsCounting | Medium | Hall & Knight | multinomialdistribution | |
| 864 | Words Beginning with a CapitalCounting | Medium | Hall & Knight | selectionordering | |
| 867 | Arranging a rowing crewCounting | Medium | Hall & Knight | restricted positionsarrangements | |
| 870 | Crew for an eight‑oared boatCounting | Medium | Hall & Knight | selectionrestricted seats | |
| 871 | Signs with no adjacent negativesCounting | Medium | Hall & Knight | combinationsarrangements | |
| 875 | Arranging coloured billiard ballsCounting | Medium | Hall & Knight | multinomial coefficient | |
| 876 | Flag hanging arrangementsCounting | Medium | Hall & Knight | multinomial coefficient | |
| 877 | Million‑plus numbers from digitsCounting | Medium | Hall & Knight | permutations with leading zero restriction | |
| 878 | Algebra word with vowel‑consonant orderCounting | Medium | Hall & Knight | permutations with fixed subsequences | |
| 887 | Distributing identical booksCounting | Medium | Hall & Knight | multinomialpermutations of multiset | |
| 889 | Awarding six distinct prizesCounting | Medium | Hall & Knight | permutationsordered selection | |
| 892 | Selections of fruitCounting | Medium | Hall & Knight | product ruleinclusion‑exclusion | |
| 893 | Dividing objects into equal groupsCounting | Medium | Hall & Knight | multinomial coefficient | |
| 895 | Permutations of "series"Counting | Medium | Hall & Knight | block methodarrangements | |
| 896 | Planes determined by pointsCounting | Medium | Hall & Knight | countinggeometry | |
| 897 | Selections from multiple copiesCounting | Medium | Hall & Knight | countingmultisets | |
| 898 | Permutations from "examination"Counting | Medium | Hall & Knight | permutationsrepetition | |
| 899 | Sum of odd‑digit numbersCounting | Medium | Hall & Knight | countingdigit sums | |
| 900 | Sum of even‑digit numbersCounting | Medium | Hall & Knight | countingdigit sums | |
| 901 | Combinations with repeated itemsCounting | Medium | Hall & Knight | identical objectscombinations+1 | |
| 902 | Maximum permutations of binary lettersCounting | Medium | Hall & Knight | permutationsbinary strings+1 | |
| 903 | Factors of a prime‑power productCounting | Medium | Hall & Knight | prime factorisationdivisors+1 | |
| 914 | Arrangements of independenceCounting | Medium | Hall & Knight | permutationsrepeated letters | |
| 915 | Arrangements of superstitiousCounting | Medium | Hall & Knight | permutationsrepeated letters | |
| 916 | Arrangements of institutionsCounting | Medium | Hall & Knight | permutationsrepeated letters | |
| 918 | Seating Americans and Englishmen alternatelyCounting | Medium | Hall & Knight | circular arrangementsgap method | |
| 919 | Number of lines from pointsCounting | Medium | Hall & Knight | lines from pointssubtract collinear cases | |
| 920 | Number of triangles from pointsCounting | Medium | Hall & Knight | triangles from pointsexclude collinear triples | |
| 921 | Selections from "expression"Counting | Medium | Hall & Knight | combinationsrepetition | |
| 922 | Arrangements from "expression"Counting | Medium | Hall & Knight | permutationsrepetition | |
| 1541 | Multinomial Coefficient 4Counting | Medium | Hall & Knight | Multinomial TheoremCoefficients | |
| 1543 | Trinomial Coefficient 2Counting | Medium | Hall & Knight | Multinomial TheoremPolynomial Expansion | |
| 15 | Two subsets, one sumCounting | Deep | Lemma | PigeonholeCounting subsets+1 | |