169 questions · 29 question types identified
Questions involving graphical solutions to linear programming problems, constraint satisfaction, or finding optimal solutions through graphical methods or simplex-type approaches.
A question is this type if and only if it involves arranging digits to form numbers with constraints (e.g., 'even numbers between 3000 and 5000').
A question is this type if and only if it requires arranging letters/objects with specific items in fixed positions (e.g., 'E at beginning and end', 'R in central position').
A question is this type if and only if it requires certain items to be together (adjacent) in the arrangement.
A question is this type if and only if it requires all items of certain categories to be grouped together (e.g., 'all vowels together and all consonants together').
A question is this type if and only if it involves arranging multiple identical objects of different types (e.g., 'identical red, blue, and yellow mugs').
Questions asking for the probability that items appear in a specific correct order or nearly correct order among all possible arrangements.
A question is this type if and only if it requires alternating types of items (e.g., consonant-vowel-consonant pattern, or no two of same type adjacent).
A question is this type if and only if it asks for the number of ways to select items with constraints on how many of each type (e.g., 'at least one M and exactly one E').
Questions asking for the number of arrangements of letters from a word containing repeated letters, with no additional constraints beyond arranging all or some of the letters.
Questions requiring certain items to NOT be together or adjacent, solved by subtracting 'together' arrangements from total arrangements or using gap methods.
Questions asking for the probability that specific items are NOT together or are separated (e.g., no two men next to each other, vowels not all together).
Questions about sorting algorithms (bubble sort, quick sort) or searching algorithms (binary search) applied to lists of numbers or names, including analysis of algorithm steps and iterations.
A question is this type if and only if it involves arranging people into multiple groups, rows, or teams with specific composition requirements.
A question is this type if and only if it involves forming codes or passwords from letters and/or digits with repetition constraints.
Questions asking for the probability that specific named items or groups are adjacent/next to each other in an arrangement.
A question is this type if and only if it involves arranging people in a line with constraints about who stands next to whom or in what positions.
Questions requiring exactly a specific number of letters between two particular items, solved by fixing positions with the required gap.
A question is this type if and only if it involves arranging people in specific seating configurations (e.g., minibus seats, rows) with positional constraints.
A question is this type if and only if it involves arranging people where some are couples/pairs with constraints about partners standing together or apart.
Questions asking for the number of ways to select a specified number of items from multiple distinct categories where each category has a minimum or maximum constraint (e.g., select 2 pop CDs, 2 jazz CDs, and 1 classical CD).
Questions requiring at least or at most a specific number of letters between items, typically solved by casework or complementary counting.
Questions asking for the probability of an alternating arrangement pattern between two types of items.
Questions about graph properties, Eulerian paths, spanning trees, network algorithms (Kruskal's, etc.), or graph construction with specified vertex orders and arcs. These are pure graph theory questions not involving assignment or matching of people to tasks.
A question is this type if and only if it asks for a conditional probability given information about an arrangement (e.g., 'probability given that certain items are together').
Questions with multiple simultaneous separation requirements (e.g., some items together AND other items not together, or fixed ends with separation constraints).
Questions where people/teams must be assigned to tasks/jobs/locations with numerical costs or scores in a table, requiring finding the optimal (minimum cost or maximum score) assignment using the Hungarian algorithm or similar methods.
| \multirow{2}{*}{} | Number of chances created per match | |||||||
| Rocinate | Quince | |||||||
| Number | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 |
| Probability | \(\frac { 1 } { 20 }\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 6 }\) | \(\frac { 1 } { 6 }\) |
| Probability of converting a chance into a goal | |
| Rocinate | Quince |
| 0.1 | 0.12 |
Questions asking for arrangements of digits (not letters) from a number with repeated digits, where the resulting number must satisfy a divisibility or parity condition (e.g., even numbers).
Questions involving bipartite graphs or tables where people/workers must be matched to tasks/jobs with constraints on who can do what, typically requiring determination of whether a complete matching exists or finding all possible matchings through systematic enumeration. No optimization of costs/scores involved.