Scheduling puzzles for SBI PO

A scheduling puzzle places people or events on days of the week, months of the year or dates in a month. Underneath, it is a linear arrangement with time as the line: Monday comes before Tuesday just as seat 1 comes before seat 2. What makes these puzzles harder than they look is the extra layer of facts the clues lean on: which months have 31 days, whether the week starts on Monday or Sunday, and which dates are odd or even.

This guide covers those facts, the method, one fully worked SBI PO-level puzzle and a practice puzzle with months and dates.

Facts to have ready

• Week order. Most puzzles run Monday to Sunday. Some start on Sunday, and some use only five working days. Read the first line carefully.
• Months with 31 days: January, March, May, July, August, October and December.
• Months with 30 days: April, June, September and November.
• February has 28 days, or 29 in a leap year.
• "Immediately after" means the very next day, month or date slot. "After" means any later time.
• "Only two people have events between A and B" means their slots differ by three.

The case-building method

1. Draw the time line as a column: days, months or month-date slots, earliest at the top.
2. Place definite clues first, such as "the Biology lecture is on Sunday".
3. Branch on the first clue with a few options. Write each case as its own column.
4. Test each new clue on every open case. A case that runs past the end of the week or month is dead.
5. Carry live cases into the second variable. Sometimes a case survives all the person clues and dies only when you place subjects or cities.
6. Check every clue against the final table.

An SBI PO-level puzzle: seven days, two variables

Seven people, J, K, L, M, N, O and P, each give one lecture on a different day of one week, from Monday to Sunday. Each lecture is on a different subject: Maths, English, History, Physics, Chemistry, Biology and Economics.

1. Only two people give lectures between J and O, and O's lecture is after J's.
2. J's lecture is after Monday and before Friday.
3. The Maths lecture is on the day immediately before O's lecture.
4. K gives the Maths lecture.
5. Only one person gives a lecture between K and M, and M's lecture is after K's.
6. N's lecture is on the day immediately after J's.
7. Only one person gives a lecture between P and N.
8. The Biology lecture is on Sunday.
9. The Chemistry lecture is on the day immediately after the Maths lecture.
10. The Physics lecture is on the day immediately after the History lecture, and the English lecture is on the day immediately after the Physics lecture.
11. The Economics lecture is on a day before the History lecture.

Step 1: branch on J. Clue 2 allows Tuesday, Wednesday or Thursday. Clue 1 puts O three days later, clues 3 and 4 put K (Maths) the day before O, and clue 5 puts M two days after K.

In Case 3, M would need to be two days after Saturday, which is outside the week. Case 3 fails.

Step 2: N and P. N is the day after J (clue 6).

• Case 1: N on Wednesday. Monday and Sunday are left for L and P. P must have one day between P and N: Monday works (Tuesday lies between). So P is on Monday and L on Sunday.
• Case 2: N on Thursday. Monday and Tuesday are left. Only Tuesday has exactly one day (Wednesday) between it and Thursday, so P is on Tuesday and L on Monday.

Both cases survive every person clue. This is where many candidates guess. Do not; carry both into the subjects.

Step 3: subjects in Case 1. Maths is Thursday, so Chemistry is Friday (clue 9), and Biology is Sunday (clue 8). History, Physics and English must fall on three days in a row (clue 10). The free days are Monday, Tuesday, Wednesday and Saturday, and the only run of three is Monday to Wednesday. That leaves Economics on Saturday, after History, which breaks clue 11. Case 1 fails.

Step 4: subjects in Case 2. Maths is Friday, so Chemistry is Saturday; Biology is Sunday. Monday to Thursday are free. The run of three can be Monday to Wednesday (Economics on Thursday, after History: fails) or Tuesday to Thursday (Economics on Monday, before History: works). So History is Tuesday, Physics Wednesday, English Thursday and Economics Monday.

A check of every possible arrangement confirms that this is the only one that satisfies all eleven clues.

Questions:

1. Which subject does N teach?
2. Who lectures on Tuesday, and on which subject?
3. How many lectures fall between L's and K's?
4. On which day is the Chemistry lecture, and who gives it?
5. Whose lecture is immediately before M's?

Answers:

1. English.
2. P, History.
3. Three: Tuesday, Wednesday and Thursday.
4. Saturday, O.
5. O's.

Month and date puzzles

For months, draw one row per month in calendar order, or only the months the puzzle names. When each month has two dates, split each row into two slots. Clues like "in a month with 30 days" or "on an even date" rule out whole rows at once, so use them early.

Common mistakes

• Starting the week on the wrong day. If the puzzle says Sunday to Saturday, Sunday is day 1.
• Letting a case run past the end. A lecture "two days after Saturday" does not exist in a Monday–Sunday week.
• Reading "after" as "immediately after".
• Forgetting which months have 30 days. A knuckle count or the list above takes two seconds.
• Dropping a case before the second variable is placed.

Practice puzzle

Six people, U, V, W, X, Y and Z, each have one event. The events fall in April, July and October of the same year, on the 8th or the 19th, with one event on each of these six dates.

1. U's event is on the 19th of a month that has 31 days.
2. Only two people have events between U's and X's.
3. X's event is in a month that has 30 days.
4. Z's event is immediately before U's.
5. W's event is on the 8th of a month.
6. Y's event is after V's.

Questions:

1. Who has the event on 19 April?
2. On which date is Y's event?
3. How many events fall between X's and W's?
4. Whose event is on 8 July?

Answers:

1. V. The slots in order are 8 Apr, 19 Apr, 8 Jul, 19 Jul, 8 Oct and 19 Oct. U is on 19 Jul or 19 Oct. If U were on 19 Oct, X would be on 8 Jul, but July has 31 days. So U is on 19 Jul and X on 8 Apr, three slots earlier. Z is on 8 Jul. W takes the only free 8th, 8 Oct. V and Y take 19 Apr and 19 Oct, with Y later.
2. 19 October.
3. Three: V, Z and U.
4. Z.

What to do next

• Redo the seven-day puzzle from a blank page, writing all three cases, in under 7 minutes.
• Solve three month-and-date puzzles this week, writing the slots as one list first.
• Move on to linear seating, which uses the same line with left and right added, and revise floor puzzles.