Grouping

• How classification and grouping puzzles assign items to categories under constraints.
• To use Venn-style or partition tables when items belong to exactly one group vs multiple groups.
• To handle inclusion/exclusion ("at least one", "none", "both") in set-based grouping.
• To solve team-selection and hobby-matching problems common in Class 11 reasoning papers.

Level 1 — Foundations

Verbal: Grouping means sorting n items into labelled buckets (Team A/B, Subject choices, Colour groups) so every rule is satisfied.

Single-group vs multi-group:

Standard clues translated:

• "A and B together" → same group.
• "A and B never together" → different groups.
• "At least one doctor in Team 1" → count constraint on group.
• "More boys than girls in Group X" → inequality on group size.

Process: List groups as columns, entities as rows. Mark ✓ (must be), ✗ (cannot be), ? (unknown). When a row has only one ?, it is forced.

Level 2 — Exam depth

Pigeonhole reasoning: If 5 students pick among 3 clubs and each club needs at least 1 member, someone shares a club — useful for "must be true" questions.

Minimum/maximum group size: Clues like "Group Red has at most 2" cap ticks in that column. Combine with total headcount.

Chain grouping: If A with B, B with C, and A not with D → A,B,C same group; D elsewhere.

Exam traps: "Neither A nor B in Group 1" means both absent from Group 1, not that they share Group 2.

Olympiad extension: Weighted grouping — each item has a score; maximise team score with category caps. Reduce to case check on who is excluded.

Split six students into two project teams under constraints

Teams: Alpha and Beta (3 each). Students: P, Q, R, S, T, U.
Clues: (1) P and Q must be together. (2) R cannot be with S. (3) T is in Alpha. (4) U is not in Beta. (5) S is in Alpha.

Step 1 — T in Alpha, S in Alpha → Alpha already has T, S + one more.
Step 2 — U not in Beta → U in Alpha. Alpha full: {T, S, U}.
Step 3 — Beta = {P, Q, R} — P,Q together ✓. R not with S ✓ (S in Alpha).
Step 4 — Verify sizes 3+3 ✓. **Alpha: T,S,U | Beta: P,Q,R**.

Use inclusion–exclusion on hobbies

40 students: 22 play cricket, 18 play chess, 10 play both.
Only-cricket = 22−10 = 12. Only-chess = 18−10 = 8. Neither = 40−(12+8+10) = 10.
Grouping puzzle link: "both" means overlap region in Venn — always subtract intersection once.

• Three friends choose Hindi, Sanskrit, or French — each one subject. Clue: A≠French, B≠Hindi. List possibilities.
• 8 items into 2 equal groups with A,B separated — how many slots left after placing A?
• Translate "exactly two of the five are doctors" into a counting rule.
• Stretch: 4 groups of 2 from 8 people with 4 married couples not separated — outline approach.

Revision tip: Revisit adjacent topics in Analytical Reasoning before mixed practice on Grouping.

Open the Practice tab for graded questions on Grouping.

Before marking ticks, write group capacity limits at the top of the page (e.g. "3 per team"). When clues mix positive and negative pairs, process all must-together chains first, then apply cannot-together crosses — reversing the order creates false eliminations. If asked "who must be in Group A?", scan for rows where every other group has a ✗. Practice Venn overlap questions separately from partition puzzles; exam headers rarely label the type explicitly.