Puzzles: Schedules, Floors, Boxes, Comparison and Tabulation

IBPS and SBI name the Reasoning test for IBPS Clerk, SBI Clerk, IBPS PO, SBI PO and IBPS RRB without publishing a topic list, and floor, box, schedule, comparison and tabulation puzzles are a standard set type in it. This chapter extends the elimination-grid method taught in the foundation reasoning chapters. It teaches the grid at bank speed, floors and stacked boxes with their counting formulas, day, month and date schedules with the odd-day arithmetic behind them, three-variable conditional puzzles with rules such as "if", "only if" and "never together", greater-than comparison puzzles with ranks, and tabulation puzzles with several attributes. Each example is complete in itself, and every puzzle in the practice questions was solved in full to confirm that exactly one answer follows.

The Elimination Grid at Bank Speed

Every puzzle in this chapter is a set of items (persons, boxes, days) to be matched to slots (floors, positions, dates). Draw a grid with items down the side and slots across the top. Each clue does one of three jobs: it fixes a cell (tick it and cross the rest of its row and column), it excludes cells (cross them), or it links two items ("the Cash clerk is on a higher floor than the Loans clerk") and has to wait until one end of the link is known. Whenever a row or a column has one blank left, that cell is forced, and the forcing spreads.

Three jobs a clue can do
Clue type	What to do	Example
Fix	Tick, then cross row and column	"M works on the top floor"
Exclude	Cross only that cell	"N is not in Loans"
Link	Write the pair and move it as a unit	"X is immediately above Y"

⚠️ Quantity words

"Exactly", "at least" and "at most" are different. "Exactly two persons are taller than D" fixes D's rank at third from the top; "at least two" only says D is third or lower. Read the quantity word before you draw a cell, and when a clue says "does not", cross; do not place.

Floors and Stacked Boxes

In a floor puzzle the stem says which floor is numbered 1, almost always the lowest. In a stack of boxes, give position 1 to the bottom box and read "above" as a larger number. The counting formulas are the same as for a row. With n floors or n boxes, the k-th from the top is (n − k + 1)-th from the bottom, and the number of floors or boxes between the places a and b is |a − b| − 1, never |a − b|.

Worked example. Seven boxes are stacked. Box X is 3rd from the top and box Y is 2nd from the bottom. X is 7 − 3 + 1 = 5th from the bottom, so between positions 5 and 2 there are 5 − 2 − 1 = 2 boxes. Worked puzzle. Five boxes S, T, U, V, W are stacked. S is at the bottom, W is at the top, T is immediately above S, and V is above U. Then T is 2nd, W is 5th, and U and V fill positions 3 and 4 with V above U, so the stack from the bottom is S, T, U, V, W and exactly one box lies between T and V.

🧠 Gap plus one

Use "between" and "immediately above" together. "Exactly two boxes between D and F" with D at the bottom puts F at position 4, because the gap of two boxes plus F itself is three steps up from D. Convert every gap to a difference of positions (gap + 1) first, then place.

Days, Months and Dates

Day puzzles are arithmetic on a cycle of seven. Number the days Monday = 1 up to Sunday = 7 (Sunday as 0 also works) and move by a number of days modulo 7: after 100 days from Wednesday you move 100 mod 7 = 2 days and reach Friday. "The day after tomorrow" is two days ahead and "three days ago" is three days back. For schedules, the same idea gives a line of seven slots: Monday to Saturday are six slots, and "immediately after" means the next slot.

Month lengths and the day shift they cause
Month group	Days	Odd days (days mod 7)
January, March, May, July, August, October, December	31	3
April, June, September, November	30	2
February	28 (29 in a leap year)	0 (1 in a leap year)

Same date, later month. The weekday of the same date moves forward by the odd days of the months passed. Worked example: 10 January is a Friday in a non-leap year. January (3) and February (0) give 3 odd days, so 10 March is Friday + 3 = Monday. In a leap year February adds 1, giving 4 odd days and Tuesday. Counting weekdays: a 30-day month is 4 weeks plus 2 extra days, and a 31-day month is 4 weeks plus 3 extra days. A 31-day month beginning on a Saturday therefore has five Saturdays, five Sundays and five Mondays, because the extra days are the first ones.

⚠️ Months and dates are lines, not cycles

Do not use the 7-day cycle for month schedules. When five events fall in five different months, the months are slots on a calendar line, and "three months after" is a difference of three on that line, which may skip months that have no event. Also, when the dates are given as numbers (3, 8, 11, 17, 24), read "seven days after" as date + 7, not as the next listed date.

Three-Variable Conditional Puzzles

A conditional puzzle gives a pool of candidates and rules, and asks who can or must be chosen. Translate every rule into one of four shapes. Together rule: "P and Q are never chosen together" means P and Q are not both in. If-then: "if R then S" forbids R without S, and its contrapositive "no S means no R" is the form that is often needed. Only if: "T only if P" means T cannot be in without P, so it behaves exactly like "if T then P". Exactly k: the team has exactly k members, so choose by elimination.

Worked example. Choose three of five officers P, Q, R, S, T so that (i) P and Q are not chosen together, (ii) if R is chosen then S is chosen, (iii) T is chosen only if P is chosen. T needs P, and P forbids Q, so a team with T is P, T and one of R or S; R would need S, which is a fourth member, so the team is P, S, T. Without T, the team is three of P, Q, R, S with rule (i): P, R, S or Q, R, S (P, Q, R and the other pairs fail a rule). The valid teams are therefore PRS, PST and QRS, and exactly one of P and Q is present in each.

🧠 Intersection and union of valid teams

List all valid teams once, then answer every question from the list. With three chosen from five or six there are at most 20 combinations, and the rules prune it to a handful. "Who must be in" is the intersection of the valid teams, "who can be in" is their union. This also makes the number of valid teams easy to count, which is a favourite question.

Greater-Than Comparison Puzzles

A comparison puzzle gives pairs such as "A is taller than B" and asks who is tallest, who is second, or whether a relation is certain. Build a chain: draw an arrow from the taller to the shorter, join the pieces through shared names, and read the order off the longest path. Two facts are easy to lose. A relation is certain only when a path of arrows joins the two persons; two persons on different branches have no certain order. And in a group of n with distinct heights, a person's rank from the top plus rank from the bottom is n + 1.

Worked example. Seven persons have distinct heights and exactly two are taller than Rita. Rita is 3rd from the tallest, so she is 7 − 3 + 1 = 5th from the shortest. Worked puzzle. Five persons A to E: exactly two are shorter than A; B is taller than A; D is taller than C and C is taller than E; B is taller than D. A has exactly two below, so A is 3rd from the top. The persons above A are B and one more, and the chain D, C, E allows only D to be that one (if C or E were above A, D would be too, making three above A). B is taller than D, so the order is B, D, A, C, E and the second tallest is D.

⚠️ Definite versus possible

When a question asks "which statements are definitely true", a relation that holds in the picture you drew is not enough. If A > B and C > B, then A and C are both above B but have no certain order between them: A > C can be true and still not be definite. Write the unknown pair down as "cannot say" instead of guessing.

Tabulation Puzzles and the Traps

A tabulation puzzle gives each item several attributes, say a person, a floor and a counter, and the grid has more than one block. Fix the attribute that carries order (days, floors) first, because order clues place items by counting. Then tie the other attributes to those slots one clue at a time. Worked example. Asha, Bimal and Charu sit on floors 1 to 3 and handle Cash, Loans and Deposits. Asha does not handle Cash; the Loans clerk is on a higher floor than the Cash clerk; Bimal is on floor 2 and does not handle Loans; Charu is not on floor 1. Charu is on floor 3 and Asha on floor 1. Asha is not Cash and cannot be Loans (nobody is below her), so Asha has Deposits. Bimal is not Loans, so Bimal has Cash and Charu has Loans.

The finished table of the worked example
Floor	Person	Counter
3	Charu	Loans
2	Bimal	Cash
1	Asha	Deposits

Order first: place the ordered attribute before the unordered ones.
Linked clues wait: do not guess an end of a link; write the pair and revisit it.
Two-case clues: if a clue leaves two cases, both stay until a later clue kills one; a question then asks only what both share.
Check at the end: re-read each clue against the finished table; a single violated clue invalidates every answer.

Key takeaways

Use an elimination grid: tick and cross a fixed cell, cross an excluded one, write a link as a pair, and let single blanks force cells; read the quantity word (exactly, at least, at most) first.
In a stack or on floors, k-th from the top is (n − k + 1)-th from the bottom and the number between two places is |a − b| − 1; convert every "gap" to gap + 1 places.
Days run on a cycle of seven: move by the days mod 7; months of 31 days shift the weekday by 3 and those of 30 days by 2; a 31-day month has three days that occur five times.
Translate each conditional rule to a shape (together, if-then, only if, exactly k), list every valid team once, and take the intersection for who must be in and the union for who can be in.
In comparison puzzles, a relation is certain only along a path of arrows; rank from the top plus rank from the bottom is n + 1; two persons on different branches have no certain order.
In tabulation, fix the ordered attribute first, attach the others one clue at a time, keep two-case clues alive, and re-check every clue against the finished table.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

If the day after tomorrow is Friday, what day was it three days ago?
1. Monday
2. Saturday
3. Sunday
4. Tuesday
Show answer
Answer: C — Sunday
The day after tomorrow is Friday, so today is Wednesday. Three days before Wednesday is Sunday. Monday comes from counting only two days back, and Tuesday is yesterday.
A month of 30 days begins on a Thursday. How many Fridays does it have?
1. 5
2. 4
3. 6
4. 3
Show answer
Answer: A — 5
30 days is 4 full weeks plus 2 extra days, and the extra days are the first two, Thursday and Friday. So Thursday and Friday occur five times each (Fridays on the 2nd, 9th, 16th, 23rd and 30th). Four counts only the full weeks.
Nine boxes are stacked one above the other. Box P is 3rd from the top and box Q is 2nd from the bottom. How many boxes are between P and Q?
1. 5
2. 4
3. 3
4. 6
Show answer
Answer: B — 4
P is 9 − 3 + 1 = 7th from the bottom and Q is 2nd, so 7 − 2 − 1 = 4 boxes lie between them. Five is the position difference without removing P, and 3 and 6 result from mixing top and bottom counts.
Seven persons have different heights, and exactly two of them are taller than Rita. What is Rita's position when counted from the shortest?
1. 4th
2. 3rd
3. 6th
4. 5th
Show answer
Answer: D — 5th
Two taller means Rita is 3rd from the tallest, so from the shortest she is 7 − 3 + 1 = 5th. The 3rd is her position from the tallest, and the 4th assumes that three persons are taller.
In a certain year, 15 August falls on a Monday. On which day of the week does 15 October of the same year fall?
1. Friday
2. Saturday
3. Sunday
4. Thursday
Show answer
Answer: B — Saturday
From 15 August to 15 October is 31 days (August) plus 30 days (September), which is 61 days. 61 mod 7 = 5, so Monday + 5 is Saturday. Friday results from 60 days, which forgets that August has 31 days.
Exactly two of three officers P, Q and R are selected for a panel. P and Q are never selected together. Which of the following is certain?
1. R is selected
2. P is selected
3. Q is selected
4. Neither P nor Q is selected
Show answer
Answer: A — R is selected
The possible pairs are PQ, PR and QR; PQ is forbidden, leaving PR and QR, and R is in both. P or Q alone is not certain, since either may be left out. Neither P nor Q would leave one person, which breaks the rule of exactly two.
Five officers K, L, M, N and O work on five floors of a building, numbered 1 (lowest) to 5 (top), one per floor, in five different departments: Loans, Cash, Deposits, Accounts and Care. M works on the top floor and N on the lowest. L works immediately above N. K works on a higher floor than O. K is in Deposits. The Care officer works above the Deposits officer. The Loans officer works immediately below the Accounts officer. N is not in Loans. Who works immediately above the Accounts officer?
1. L
2. M
3. N
4. K
Show answer
Answer: D — K
M is on floor 5, N on 1 and L on 2; K is above O, so O is on 3 and K on 4. K has Deposits, Care is above it (M), and Loans sits just below Accounts. N is not Loans, so Cash is N and Loans-Accounts are L (floor 2) and O (floor 3). The Accounts officer is O, and K is immediately above. L is the Loans officer, the swap that arises from reversing the Loans-Accounts pair.
Six boxes A, B, C, D, E and F are stacked one above the other. D is at the bottom. Exactly two boxes are kept between D and F, and F is above D. B is the fifth box from the bottom. F is kept immediately above A. C is kept somewhere between D and E, with D below C. How many boxes are kept between C and E?
1. 2
2. 4
3. 3
4. 1
Show answer
Answer: C — 3
D is position 1 and F is position 4, so A is 3 and B is 5. C and E are left for positions 2 and 6, and C is between D and E, so C is 2 and E is 6. The boxes between C and E are A, F and B, which is 3. Two counts only A and F.
Six auditors P, Q, R, S, T and U each inspect a branch on a different day from Monday to Saturday of one week. T inspects on the day immediately after R, and P on the day immediately after T. U inspects on Thursday. S does not inspect on the day immediately before or immediately after U. Who inspects on the day immediately after U?
1. Q
2. S
3. P
4. T
Show answer
Answer: A — Q
R, T, P run on three consecutive days, and Thursday is U's, so they must be Monday to Wednesday. Q and S take Friday and Saturday; S cannot be next to U on Friday, so S is Saturday and Q is Friday. S is the tempting answer for the last day of the week.
Five camps A, B, C, D and E were held in five different months of one year, namely January, March, May, August and October, one camp per month. D was held three months after E. B was held later than D. A was held earlier than E but later than C. Which camp was held exactly two months before camp E?
1. C
2. D
3. B
4. A
Show answer
Answer: D — A
Only May and August are three months apart, so E is May and D is August. B is later than D, so October. A and C take January and March with C before A, so C is January and A is March, exactly two months before May. C is January, four months before E.
Five officers P, Q, R, S and T attend interviews on five different dates of a month, namely the 3rd, 8th, 11th, 17th and 24th, one on each date. S was interviewed exactly 7 days after R. Q was interviewed on an even date. T was interviewed earlier than P. How many days after P's interview was R's interview held?
1. 9
2. 6
3. 14
4. 13
Show answer
Answer: B — 6
The only pair 7 days apart is 17 and 24, so R is 17 and S is 24. The only even date is 8, so Q is 8. T and P take 3 and 11 with T earlier, so P is 11 and R's date is 17 − 11 = 6 days later. Nine would measure from Q.
A team of three is chosen from six officers A, B, C, D, E and F under these rules. If A is chosen, B must be chosen. C and D are never chosen together. E can be chosen only if A is chosen. F can be chosen only if D is chosen. If C is in the team, which two others are definitely in it?
1. B and D
2. A and E
3. A and B
4. D and F
Show answer
Answer: C — A and B
With C in, D is out, so F is out (F needs D). That leaves A, B, E for the other two places. E needs A, and A needs B, so the pair is A and B, giving ABC. B and D fails as D cannot sit with C, and A and E fails as A needs B.
Five persons A, B, C, D and E have different heights. Exactly two persons are shorter than A. B is taller than A. D is taller than C, and C is taller than E. B is taller than D. Who is the second tallest of the five?
1. D
2. A
3. B
4. C
Show answer
Answer: A — D
A has exactly two below, so A is 3rd from the top. The chain D, C, E puts C and E below A, and B is above A, so the top three are B, D, A. B is the tallest because B is taller than D, so D is second. A is only third.
Four officers W, X, Y and Z work in four different departments, namely Cash, Loans, Deposits and Enquiry, and each took leave on a different day from Monday to Thursday. The Loans officer took leave on the day immediately before Z. X took leave earlier in the week than Z. The Deposits officer took leave on the day immediately before X. Exactly one day lies between the leave days of the Loans officer and the Cash officer. Y did not take leave on Monday or Thursday. In which department does W work?
1. Loans
2. Cash
3. Deposits
4. Enquiry
Show answer
Answer: B — Cash
X is earlier than Z, the Loans officer is the day before Z and the Deposits officer the day before X. This makes X the Loans officer; the only other case, X on Tuesday and Z on Thursday, leaves Cash no free day two days from Loans. So Deposits, X (Loans) and Z fall on consecutive days, and Cash is two days from X. The only fit is Deposits Tuesday, X Wednesday, Z Thursday, Cash Monday. Y cannot take Monday, so Y is Tuesday (Deposits) and W is Monday, in Cash. Loans is X, not W.
Five persons K, L, M, N and O live on five different floors of a building, numbered 1 (lowest) to 5 (top), one per floor. O lives on the third floor. K lives on a higher floor than O. O lives immediately above L. M lives on a higher floor than N. Which of the following is definitely true?
1. K lives on the top floor
2. M lives immediately above K
3. L lives above O
4. N lives on the lowest floor
Show answer
Answer: D — N lives on the lowest floor
L is on floor 2 and O on 3, leaving floors 1, 4 and 5 for K, M and N. K is above O, so K is on 4 or 5 and M is above N, so N is on floor 1; M and K share 4 and 5 in either order. N on floor 1 is the only fact common to both cases. K on top and M above K each hold in one case only.
A is taller than B. C is taller than B. B is taller than D. E is taller than C. D is taller than F. Statements. P: E is taller than F. Q: A is taller than D. R: A is taller than C. S: C is taller than F. Which of the statements are definitely true?
1. Only P and Q
2. Only Q and R
3. Only P, Q and S
4. All of P, Q, R and S
Show answer
Answer: C — Only P, Q and S
The paths are E > C > B > D > F and A > B. P, Q and S follow along these paths: E to F, A to D through B, and C to F. R has no path between A and C, since both are only above B, so it is not certain. Only P and Q wrongly drops the path C > B > D > F.