| 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 | |