In this guide
A scheduling set is an arrangement set in which the positions are points in time. Instead of seats you have days, and often slots within a day: morning and afternoon, or periods 1 to 4. On top of that there is usually a second layer, such as who conducts each session or which room it uses.
That two-layer structure is what makes CAT scheduling sets feel heavy. The fix is a grid that shows both layers at once, and the discipline to push every case forward until a clue breaks it. This guide builds that grid and works through two original sets, each checked by computer to have exactly one solution.
What makes scheduling different from seating
| Seating set | Scheduling set |
|---|---|
| Positions are seats in a row or circle | Positions are days, often split into slots |
| "Next to" works both ways | "Before" and "after" have a direction |
| One attribute per person, usually | Often a second assignment (mentor, room), with its own rules |
| "Opposite" in circles | "Same slot on another day" |
| Rarely a "no two on the same day" rule | Frequent "not twice on one day" rules for the second layer |
The words need careful translation.
| Words in the set | What it means on the grid |
|---|---|
| "X is the day after Y" | X's day = Y's day + 1 |
| "X is later in the week than Y" | X's day > Y's day, any gap |
| "X and Y are in the same slot" | Both morning or both afternoon, days unspecified |
| "X is on the day immediately before Y" | Consecutive days, X first |
| "No mentor takes two sessions on one day" | Each mentor's sessions are on different days |
The method
- Draw the grid: days as columns, slots as rows. Leave room in each cell for the second layer.
- Place fixed clues. "Tech is on Tuesday" goes straight in.
- Pair up linked items. "B is the day after S" creates a block of two that must fit together.
- List the cases for the most restrictive block, usually the one with the fewest legal placements.
- Push each case to the end or to a contradiction.
- Fill the second layer last, once the sessions are fixed.
Set 1: a warm-up across four days
Four meetings, Budget, Hiring, Sales and Tech, are held from Monday to Thursday, one per day.
- Tech is held neither on Monday nor on Thursday.
- Budget is held on the day immediately after Sales.
- Hiring is held on an earlier day than Sales.
Solution. Tech is on Tuesday or Wednesday.
- Case 1: Tech on Tuesday. Monday, Wednesday and Thursday are left. Sales and Budget need consecutive days, so they take Wednesday and Thursday. Hiring goes to Monday, which is before Sales. This works.
- Case 2: Tech on Wednesday. Monday, Tuesday and Thursday are left. The only consecutive pair is Monday–Tuesday, so Sales is Monday and Budget Tuesday. Hiring would be Thursday, after Sales. This breaks clue 3.
| Day | Mon | Tue | Wed | Thu |
|---|---|---|---|---|
| Meeting | Hiring | Tech | Sales | Budget |
Sales and Budget formed a block of two, and the block had only one legal place in each case. Blocks are the fastest way into a scheduling set.
Set 2: sessions, slots and mentors
A coaching centre schedules six sessions (Algebra, Arithmetic, DI, Geometry, Para-jumbles and RC) from Monday to Wednesday, two per day: one in the morning and one in the afternoon. Three mentors, X, Y and Z, take two sessions each, and no mentor takes both sessions on the same day.
- Geometry is in a morning slot, but not on Monday.
- DI is in an afternoon slot, on the day immediately before Geometry.
- RC is on the day immediately after Arithmetic, in the same slot as Arithmetic.
- Algebra is on an earlier day than Para-jumbles.
- Arithmetic and Algebra are on different days.
- X takes Geometry and RC.
- Y takes DI, and Y takes no session on Wednesday.
Step 1: two cases from clue 1. Geometry is on Tuesday morning or Wednesday morning, and clue 2 puts DI on the afternoon of the day before.
Step 2: Case A, Geometry on Wednesday morning. DI is on Tuesday afternoon. Now place the Arithmetic–RC block (consecutive days, same slot):
- Arithmetic Monday morning, RC Tuesday morning: both free. Possible.
- Arithmetic Monday afternoon, RC Tuesday afternoon: Tuesday afternoon is DI. No.
- Arithmetic Tuesday morning, RC Wednesday morning: Wednesday morning is Geometry. No.
So Arithmetic is Monday morning and RC Tuesday morning. Monday afternoon and Wednesday afternoon remain for Algebra and Para-jumbles, and clue 4 puts Algebra on Monday. But then Arithmetic and Algebra are both on Monday, which breaks clue 5. Case A fails.
Step 3: Case B, Geometry on Tuesday morning. DI is on Monday afternoon. Place the block again:
- Arithmetic Monday morning, RC Tuesday morning: Tuesday morning is Geometry. No.
- Arithmetic Tuesday afternoon, RC Wednesday afternoon: both free. Possible.
Monday morning and Wednesday morning remain. Clue 4 puts Algebra on Monday morning and Para-jumbles on Wednesday morning. Clue 5 holds: Algebra is Monday, Arithmetic Tuesday.
Step 4: the mentors. X takes Geometry (Tuesday) and RC (Wednesday), on different days as required. Y takes DI (Monday) and one more session, which cannot be on Monday (same day as DI) or on Wednesday (clue 7). On Tuesday, the morning is X's Geometry, so Y takes Arithmetic on Tuesday afternoon. Z takes the rest: Algebra (Monday) and Para-jumbles (Wednesday).
| Slot | Monday | Tuesday | Wednesday |
|---|---|---|---|
| Morning | Algebra (Z) | Geometry (X) | Para-jumbles (Z) |
| Afternoon | DI (Y) | Arithmetic (Y) | RC (X) |
Q1. Which session is on Tuesday afternoon? Arithmetic.
Q2. Who takes Para-jumbles? Z.
Q3. How many of Z's sessions are in the morning? Two (Algebra and Para-jumbles).
Q4. If clue 5 were removed, how many complete schedules (sessions and mentors) would be possible? Case A comes back. In Case A, X takes RC (Tuesday) and Geometry (Wednesday); Y takes DI on Tuesday and must take a Monday session, Arithmetic or Algebra; Z takes the other Monday session and Para-jumbles. That gives two Case A schedules plus the Case B schedule: 3.
Common mistakes
- Reading "earlier in the week" as "the day before". Clue 4 allows any gap; clue 2 does not.
- Ignoring the slot in "same slot". Clue 3 fixes both day gap and slot, which is why most placements of the block failed.
- Filling mentors too early. Mentor rules depend on days. Fix the sessions first unless a mentor clue is the only anchor.
- Forgetting the implicit rule. "No mentor takes both sessions on one day" is stated once in the introduction, and it was needed to place Y's Arithmetic.
- Not writing Case A down. Case A survived three clues before failing. Solving it in your head is how people end up with the wrong grid.
Practice set
- In set 1, suppose clue 1 said only "Tech is not held on Monday". How many schedules would be possible?
- In set 2, suppose clue 7 is removed entirely. In how many ways can the mentors be assigned?
- In set 2, on which day does X take no session?
Answers:
- Two. Tech on Thursday is now allowed: Hiring, Sales, Budget, Tech (Monday to Thursday) satisfies clues 2 and 3, alongside the original schedule.
- Four. Case A broke on clue 5, not clue 7, so the session grid is unchanged. X keeps Geometry and RC. Y and Z now share Algebra and DI (both Monday) and Arithmetic and Para-jumbles (Tuesday and Wednesday). Neither can take both Monday sessions, so one takes Algebra and the other DI: 2 ways. The Tuesday and Wednesday sessions are on different days, so either split works: 2 ways. That is 2 × 2 = 4, confirmed by a computer check.
- Monday. X's sessions are on Tuesday and Wednesday.
What to do next
- Redraw set 2 from memory tomorrow and solve it again without looking.
- For each new scheduling set, circle the "blocks" (pairs of linked sessions) before placing anything.
- Practise translating "the day after", "later in the week" and "same slot" until the grid move is automatic.
- Revisit arrangement sets for case splitting, and read DILR time management to decide how long a two-layer set deserves.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Indian Institutes of Management website .
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