Scheduling puzzles (days, months, years) for IBPS PO

A scheduling puzzle is a floor puzzle turned on its side. Instead of floors, you have a timeline: days of a week, months of a year, or dates within months. The logic of "immediately before", "after" and "only two between" is the same. What changes is that the timeline has features of its own, such as which months have 30 days, which days are the weekend, or a slot that nobody takes.

In IBPS PO, scheduling puzzles usually come as a set of four or five questions and often carry a second variable, such as a subject, a city or a company. The method below works for all of them.

Setting up the timeline

1. Write the slots in order, top to bottom: Monday to Sunday, January to December, or each date in order.
2. Note the timeline's features beside it: the week starts on Monday unless stated otherwise; months with 31 days (January, March, May, July, August, October, December); months with 30 days (April, June, September, November); February with 28 or 29.
3. Mark empty slots when there are more slots than people.
4. Add a column for every extra variable.

Reading the clues

The case-building method

1. Place the anchors: fixed days, fixed dates, or "on the last day".
2. When a clue allows two slots, write Case 1 and Case 2 side by side.
3. Push each case with every clue. Kill a case the moment a clue fails.
4. Fill the second variable last, using chains ("Forex is immediately before Loans") and negative clues.
5. Check every clue before answering.

Worked set 1: days and workshops

Seven people, L, M, N, O, P, Q and R, each attend a workshop on a different day of one week, from Monday to Sunday. The week starts on Monday. Each attends a different workshop: Accounts, Audit, Credit, Forex, Loans, Risk and Treasury.

1. Only two people attend between M and the one who attends Credit.
2. M attends on a day after Thursday.
3. The Audit workshop is on Wednesday.
4. L attends Credit.
5. N attends after L, with only one person between them.
6. P attends on the day immediately after M.
7. R attends on a day after Q. Q does not attend on Monday.
8. The Forex workshop is immediately before the Loans workshop, and the Risk workshop is immediately after the Loans workshop.
9. The Accounts workshop is on Saturday or Sunday.

Building the cases

• Clue 2: M attends on Friday, Saturday or Sunday.
• Clue 1: Credit is three days before M (three days after is past Sunday). So Credit is on Tuesday, Wednesday or Thursday.
• Clue 3: Wednesday is Audit. So Case 1: M = Friday, Credit = Tuesday or Case 2: M = Sunday, Credit = Thursday.
• Clue 6: P attends the day after M. In Case 2, M is on Sunday and there is no day after. Case 2 fails.

Finishing Case 1

• M = Friday, P = Saturday. L attends Credit on Tuesday (clue 4).
• Clue 5: N is two days after L, so N = Thursday.
• Monday, Wednesday and Sunday remain for O, Q and R.
• Clue 7: Q is not on Monday, and R is after Q. If Q = Sunday, R has no later day. So Q = Wednesday (Audit), R = Sunday and O = Monday.
• Clue 8: Forex, Loans and Risk are three days in a row. Tuesday and Wednesday are taken, so the run is Thursday–Friday–Saturday or Friday–Saturday–Sunday.
• Clue 9: Accounts must be on Saturday or Sunday. The second run would leave only Monday or Thursday for Accounts. So the run is Thursday–Friday–Saturday: N Forex, M Loans, P Risk.
• Accounts goes to Sunday (R), and Treasury to Monday (O).

Questions

1. Who attends the Risk workshop? P.
2. On which day is the Forex workshop? Thursday.
3. How many people attend between O and N? Two (L and Q).
4. Which workshop does the person who attends immediately after Q attend? Forex (N).
5. Who attends on the last day of the week, and which workshop? R, Accounts.

Worked set 2: dates in months

Six people, B, C, D, E, F and G, each have a meeting on a different date. The meetings fall on the 12th and the 25th of March, June and September of the same year, so there are six slots in this order: 12 March, 25 March, 12 June, 25 June, 12 September, 25 September.

1. C's meeting is on the 12th of a month that has 30 days.
2. Only two meetings are held between C's meeting and G's meeting.
3. B and F have meetings in the same month, and F's meeting is after B's.
4. Only one meeting is held between D's meeting and B's meeting.

Building the cases

• Clue 1: June and September have 30 days, so C is on 12 June or 12 September.
• Clue 2: G is three slots from C. If C = 12 June, G = 25 September. If C = 12 September, G = 25 March. So Case 1: C = 12 June, G = 25 September and Case 2: C = 12 September, G = 25 March.
• Clue 3: B and F need both slots of one month. In Case 1, only March is fully free, so B = 12 March and F = 25 March. In Case 2, only June is fully free, so B = 12 June and F = 25 June.
• Clue 4: D is two slots from B. In Case 1, B is the first slot, so D would be 12 June, which is C's. Case 1 fails. In Case 2, D is 12 March or 12 September; 12 September is C's, so D = 12 March.
• E takes the last free slot, 25 September.

Questions

1. Whose meeting is on 25 June? F.
2. How many meetings are held between D's and C's? Three (G, B and F).
3. Who has a meeting in the same month as C? E.
4. Whose meeting is immediately before B's? G.

Common mistakes

• Wrapping the week around. Unless the puzzle says so, Sunday is not "before" Monday.
• Forgetting empty slots when counting "between". An empty day still counts as a day.
• Guessing month lengths. Write the 30-day months beside the frame before you start.
• Placing a chain without sliding it. A block of three consecutive days can often sit in two places; check both.
• Mixing up slot order and calendar order in date puzzles. Number the slots 1 to 6 first.

Practice puzzle

Six people, U, V, W, X, Y and Z, each give a lecture on a different day of one week, from Monday to Sunday. The week starts on Monday. On one day there is no lecture.

1. Y's lecture is on Thursday.
2. Only one day lies between Y's lecture and the day with no lecture.
3. U's lecture is on the day immediately before the day with no lecture.
4. Z's lecture is after V's, with only one day between them.
5. W's lecture is before Y's, but not on Monday.
6. X's lecture is before Z's.

Questions

1. On which day is there no lecture?
2. Whose lecture is on Friday?
3. How many lectures are held between W's and Z's?
4. Whose lecture is on the day immediately after the day with no lecture?

Answers

The empty day is Tuesday or Saturday, and U's lecture is the day before it. If the empty day is Saturday, U is on Friday; V and Z (two days apart) can only be Monday and Wednesday; W must then be Tuesday and X Sunday, which is after Z. That breaks clue 6. So the empty day is Tuesday and U is on Monday. W must be Wednesday (before Thursday, not Monday). V and Z are then Friday and Sunday, and X is Saturday.

1. Tuesday.
2. V.
3. Three (Y, V and X).
4. W.

What to do next

• Solve two scheduling puzzles a day for a week, alternating days and months.
• Write the 30-day months from memory until you never need to count knuckles in the exam.
• Revise floor and box puzzles for the same case method, then move on to linear seating, where left and right add a new layer.