Floor puzzles, box stacks and scheduling grids are 35 of the 692 reasoning questions the Punjab Police SI has asked. They are the same problem wearing three costumes. In each one there are n slots in a fixed order — floors of a building, boxes in a pile, days of the week — and n items to put in them, and a handful of clues that pin some items down. Because the slots are ordered, the whole thing reduces to numbering. Draw the slots, number them, place every clue that names a number, and let the rest fall out. There is no insight required anywhere in these thirty-five questions — only the discipline of writing a column instead of holding it in your head. Like seating, these come in pairs: one puzzle, two questions, printed as 39 and 40 in almost every paper.
The teaching part above and below — the explanations, the figures and the worked examples on screen — is about 10 minutes. The collapsed question banks hold 35 solved past questions in all; working through every one of them takes roughly 74 minutes. Do that across several sittings, not in one go.
Part 1 · Floors and boxes — 13 questions
One column, numbered once, and never renumbered
Draw a column of n boxes. Decide once whether 1 is the bottom or the top, write that word beside the column, and never change it. Almost every error in this part comes from a candidate who numbered from the bottom and then read a clue that counted from the top. Then the clues translate directly. Third from the bottom is slot 3. Immediately above N is one slot higher than N. Four boxes between W and Y means their slot numbers differ by five. Fill in every clue that gives an exact slot first; what is left is usually a single ordering that satisfies the rest.
k items between two slots means the slot numbers differ by k + 1. Four boxes between W and Y puts them five apart — W at 7 and Y at 2, or W at 6 and Y at 1. The answer k is printed as a distractor every single time.
Every other floor and box question (12)Tap to open
There are five books a, b, c, d and e placed on a table. If a is placed below e, c is placed above d, b is placed below a and d is placed above e, then which of the following books touches the surface of the table ? (SI 2016)
- 1c
- 2a
- 3b
- 4e
Show answer
Answer: 3 — b
Take the four clues in turn. 'a below e' gives e over a. 'b below a' puts b under a, so the bottom so far is b, a, e. 'd above e' places d over e, and 'c above d' places c on top of d. Chaining them gives one and only one stack: ```puzzle:stack 5: c 4: d 3: e 2: a 1: b ``` Only b is at floor level, so b touches the table. Option 2 (a) is the trap — a is below e but still has b underneath it.
Which box is exactly in the middle? (SI 21 Jun 2023)
- 1Y
- 2W
- 3Z
- 4V
Show answer
Answer: 3 — Z
Number the positions 1 (bottom) to 7 (top). W is topmost, so W = 7. Four boxes between W and X puts X at 7 − 5 = 2. V is bottommost, so V = 1. T is fifth from the bottom, T = 5, and Y is immediately above T, so Y = 6. Two boxes between Z and V (V = 1) puts Z = 4. The only place left for U is 3. ```puzzle:stack 7: W 6: Y 5: T 4: Z 3: U 2: X 1: V ``` With seven boxes the exact middle is position 4, which holds Z.
Which box is placed third from the bottom? (SI 21 Jun 2023)
- 1U
- 2X
- 3W
- 4Z
Show answer
Answer: 1 — U
The same stack is fixed by the clues: ```puzzle:stack 7: W 6: Y 5: T 4: Z 3: U 2: X 1: V ``` Counting from the bottom, V is first, X is second and U is third. X is the trap because it is second from the bottom, not third.
Which box is placed at the first position from the bottom? (SI 1 Jul 2023)
- 1Q
- 2T
- 3P
- 4U
Show answer
Answer: 3 — P
Number the positions 1 (bottom) to 7 (top). - V is third from the bottom → V = 3; U is immediately below V → U = 2. - "Only three boxes between Q and P" means the gap is 4 positions, and P is below Q, so Q − P = 4. With 2 and 3 taken, the only fit is P = 1, Q = 5. - Q is immediately above T → T = 4. - Positions 6 and 7 are left for R and S; R is immediately below S and S is above Q, so R = 6 and S = 7. ```puzzle:stack 1: P 2: U 3: V 4: T 5: Q 6: R 7: S ``` Position 1 (the bottom) holds P. Option 4 (U) is second from the bottom — the trap for anyone who reads "U immediately below V" as "U at the bottom".
How many boxes are placed between R and V? (SI 1 Jul 2023)
- 1Two
- 2One
- 3Three
- 4Four
Show answer
Answer: 1 — Two
Number the positions 1 (bottom) to 7 (top). - V is third from the bottom → V = 3; U is immediately below V → U = 2. - "Only three boxes between Q and P" means the gap is 4 positions, and P is below Q, so Q − P = 4. With 2 and 3 taken, the only fit is P = 1, Q = 5. - Q is immediately above T → T = 4. - Positions 6 and 7 are left for R and S; R is immediately below S and S is above Q, so R = 6 and S = 7. ```puzzle:stack 1: P 2: U 3: V 4: T 5: Q 6: R 7: S ``` R is at position 6 and V at position 3, so positions 4 (T) and 5 (Q) lie between them — two boxes. Option 3 (Three) is what you get by counting the positions from V to R inclusive of one endpoint.
How many boxes are kept between U and R? (SI 3 Jul 2023)
- 1Three
- 2Four
- 3Two
- 4One
Show answer
Answer: 1 — Three
Number the positions 1 at the bottom to 6 at the top. V is third from the bottom: V = 3, and W immediately above V gives W = 4. Three boxes between S and T with T lower means the gap is 4, so either T = 1, S = 5 or T = 2, S = 6. U must sit immediately above S, and S = 6 leaves no room above, so T = 1 and S = 5, U = 6. The only box left, R, takes the only free position, 2. ```puzzle:stack 6: U 5: S 4: W 3: V 2: R 1: T ``` U is at position 6 and R at position 2, so positions 3, 4 and 5 (V, W, S) lie between them — three boxes. Answering 'Four' counts R or U itself.
Which box is second from the bottom? (SI 3 Jul 2023)
- 1R
- 2U
- 3T
- 4E
Show answer
Answer: 1 — R
Number the positions 1 at the bottom to 6 at the top. V is third from the bottom: V = 3, and W immediately above V gives W = 4. Three boxes between S and T with T lower means the gap is 4, so either T = 1, S = 5 or T = 2, S = 6. U must sit immediately above S, and S = 6 leaves no room above, so T = 1 and S = 5, U = 6. The only box left, R, takes the only free position, 2. ```puzzle:stack 6: U 5: S 4: W 3: V 2: R 1: T ``` Position 2, counting from the bottom, holds R. T is at the very bottom and U at the very top, so both are traps for careless counting; option 4 prints 'E', which is not even one of the six boxes.
How many people live between P and S? (SI 14 Jul 2023)
- 1Three
- 2Four
- 3One
- 4Two
Show answer
Answer: 1 — Three
T is on the middle floor of seven, so T is on floor 4. Only two people live between T and R means the gap is three floors, so R is on floor 1 or floor 7; R is below T, so R is on floor 1. U is on floor 7. P is even with V directly above, so P is 2 (P = 6 would force V = 7, which is U's floor). That gives V = 3. Floors 5 and 6 are left for Q and S, and S must be even, so S = 6 and Q = 5. ```puzzle:stack 7: U 6: S 5: Q 4: T 3: V 2: P 1: R ``` P is on floor 2 and S is on floor 6, so the people between them are on floors 3, 4 and 5 — V, T and Q. That is three people. Option 2 (four) comes from counting the two end residents themselves, and option 4 (two) from reading 'only two people live between T and R' as if it applied here.
On which floor does Q live? (SI 14 Jul 2023)
- 1Floor number 2
- 2Floor number 3
- 3Floor number 5
- 4Floor number 6
Show answer
Answer: 3 — Floor number 5
T is on the middle floor of seven, so T is on floor 4. Only two people live between T and R means the gap is three floors, so R is on floor 1 or floor 7; R is below T, so R is on floor 1. U is on floor 7. P is even with V directly above, so P is 2 (P = 6 would force V = 7, which is U's floor). That gives V = 3. Floors 5 and 6 are left for Q and S, and S must be even, so S = 6 and Q = 5. ```puzzle:stack 7: U 6: S 5: Q 4: T 3: V 2: P 1: R ``` Q is never named in any clue, so Q takes whatever floor is left after everyone else is placed. Floors 1, 2, 3, 4, 6 and 7 go to R, P, V, T, S and U, leaving floor 5 for Q. Option 4 (floor 6) is the trap: floor 6 is even and unassigned for a moment, but the clue 'S lives on an even numbered floor' claims it, since the only even floors are 2, 4 and 6 and P already holds 2 while T holds 4.
Which box is kept immediately above N? (SI 29 Jul 2023)
- 1L
- 2R
- 3Q
- 4O
Show answer
Answer: 4 — O
Number the positions 1 to 7 from the top. N is third from the top, so N = 3, and L is immediately below N, so L = 4. P is somewhere below N and M is immediately below P, so P can only be 5 or 6. If P = 5 then M = 6 and the free positions are 1, 2 and 7. No two of those are four apart, so 'only three boxes between R and Q' cannot be met. Rejected. So P = 6 and M = 7, leaving positions 1, 2 and 5 free. Only 1 and 5 are four apart, so R and Q take those two positions (in either order) and O takes position 2. The stack from top to bottom is R, O, N, L, Q, P, M. ```puzzle:stack stack: R, O, N, L, Q, P, M ``` (R and Q may be swapped; neither question depends on which is which.) N sits at position 3, so the box immediately above it is at position 2, which is O. L (option 1) is immediately below N, not above it — that is the trap.
Which box is kept second from the bottom? (SI 29 Jul 2023)
- 1Q
- 2M
- 3P
- 4L
Show answer
Answer: 3 — P
Number the positions 1 to 7 from the top. N is third from the top, so N = 3, and L is immediately below N, so L = 4. P is somewhere below N and M is immediately below P, so P can only be 5 or 6. If P = 5 then M = 6 and the free positions are 1, 2 and 7. No two of those are four apart, so 'only three boxes between R and Q' cannot be met. Rejected. So P = 6 and M = 7, leaving positions 1, 2 and 5 free. Only 1 and 5 are four apart, so R and Q take those two positions (in either order) and O takes position 2. The stack from top to bottom is R, O, N, L, Q, P, M. ```puzzle:stack stack: R, O, N, L, Q, P, M ``` (R and Q may be swapped; neither question depends on which is which.) Second from the bottom of seven boxes is position 6, which is P. M (option 2) is at position 7, the bottom box itself, and that is the usual slip.
How many boxes are kept between U and V? (SI 31 Jul 2023)
- 1One
- 2Four
- 3Three
- 4Two
Show answer
Answer: 4 — Two
Number the positions 1 at the bottom to 7 at the top. Q is fifth from the bottom, so Q is 5, and T is immediately above Q, so T is 6. Only one box is below R, so R is 2. Four boxes lie between S and R, so S and R are five places apart: S is 7. P, U and V take 1, 3 and 4; P is immediately below U, so P is 3 and U is 4, leaving V at 1. ```puzzle:stack stack: S, T, Q, U, P, R, V ``` V is at position 1 and U at position 4, so the boxes in between are R (2) and P (3) — two boxes. Counting the gap as 4 - 1 = 3 places gives the trap answer 'Three'.
Part 2 · Days of the week — 14 questions
Six or seven ordered slots with names on them
These are identical to the box stack, except that the slots have names — Monday to Saturday, or Monday to Sunday — and the items are packets, lifts, tents, halls or boxes being used one per day. Write the days in a row and number them 1 to 6 or 1 to 7. From that moment nothing in the question is about days at all. The day immediately before is one slot back; exactly two between is three slots apart; the last day is slot 6 or 7. The names are decoration, and treating them as numbers removes every chance of a weekday slip. One detail is worth watching: when six items are spread over seven days, exactly one day is free, and finding which day that is usually solves the puzzle by itself.
Every other day-scheduling question (13)Tap to open
Which of these packets will be consumed on Tuesday? (SI 20 Jun 2023)
- 1Packet 2
- 2Packet 4
- 3Packet 3
- 4Packet 5
Show answer
Answer: 2 — Packet 4
Packet 1 is on Thursday (day 4) and packet 5 is on the day just before it, i.e. Wednesday (day 3). Two packets between 6 and 1 means that day(6) differs from day 4 by 3, so day(6) = 1 (Monday), since day 7 does not exist. Between 6 (Mon) and 5 (Wed) exactly one packet is consumed, so exactly one packet lies between 5 (Wed) and 3: day(3) differs from day 3 by 2, giving day 1 or day 5; day 1 is taken by packet 6, so packet 3 is on Friday. Tuesday and Saturday are left for packets 2 and 4, and packet 4 is not on Saturday, so 4 is on Tuesday and 2 on Saturday: Day · Mon · Tue · Wed · Thu · Fri · Sat Packet · 6 · 4 · 5 · 1 · 3 · 2 Tuesday carries packet 4. Option 4 (packet 5) is the trap for anyone who places 5 immediately after 6 rather than immediately before 1.
How many packets will be consumed after packet 5? (SI 20 Jun 2023)
- 1Two
- 2Four
- 3Three
- 4One
Show answer
Answer: 3 — Three
Packet 1 is on Thursday (day 4) and packet 5 is on the day just before it, i.e. Wednesday (day 3). Two packets between 6 and 1 means that day(6) differs from day 4 by 3, so day(6) = 1 (Monday), since day 7 does not exist. Between 6 (Mon) and 5 (Wed) exactly one packet is consumed, so exactly one packet lies between 5 (Wed) and 3: day(3) differs from day 3 by 2, giving day 1 or day 5; day 1 is taken by packet 6, so packet 3 is on Friday. Tuesday and Saturday are left for packets 2 and 4, and packet 4 is not on Saturday, so 4 is on Tuesday and 2 on Saturday: Day · Mon · Tue · Wed · Thu · Fri · Sat Packet · 6 · 4 · 5 · 1 · 3 · 2 Packet 5 is on Wednesday, so the packets consumed after it are on Thursday (1), Friday (3) and Saturday (2) — three packets.
On which day does K go for picnic? (SI 29 Jun 2023)
- 1Saturday
- 2Friday
- 3Monday
- 4Thursday
Show answer
Answer: 2 — Friday
N goes before Q (Tuesday), so N goes on Monday. L goes exactly after Q, so L goes on Wednesday. Thursday to Sunday are left for K, M, O and P. Exactly one friend goes between O and P with O earlier, so P is two days after O. O = Thursday gives P = Saturday; O = Friday would give P = Sunday, which is barred. So O is on Thursday and P on Saturday, leaving Friday and Sunday for K and M. K cannot go on Sunday, so K goes on Friday and M on Sunday. K after L (Wednesday) is satisfied. Day · Friend Monday · N Tuesday · Q Wednesday · L Thursday · O Friday · K Saturday · P Sunday · M K therefore goes on Friday. Saturday belongs to P and Monday to N, so options 1 and 3 are ruled out; Thursday is O's day.
How many friends go for the picnic before O? (SI 29 Jun 2023)
- 15
- 22
- 33
- 44
Show answer
Answer: 3 — 3
N goes before Q (Tuesday), so N goes on Monday. L goes exactly after Q, so L goes on Wednesday. Thursday to Sunday are left for K, M, O and P. Exactly one friend goes between O and P with O earlier, so P is two days after O. O = Thursday gives P = Saturday; O = Friday would give P = Sunday, which is barred. So O is on Thursday and P on Saturday, leaving Friday and Sunday for K and M. K cannot go on Sunday, so K goes on Friday and M on Sunday. K after L (Wednesday) is satisfied. Day · Friend Monday · N Tuesday · Q Wednesday · L Thursday · O Friday · K Saturday · P Sunday · M O goes on Thursday, and the friends before Thursday are N (Monday), Q (Tuesday) and L (Wednesday) — three friends. Counting O himself gives 4 and counting the whole rest of the week gives 5, which are the traps in options 4 and 1.
On which of the following days will lift 4 be used? (SI 2 Jul 2023)
- 1Friday
- 2Thursday
- 3Tuesday
- 4Saturday
Show answer
Answer: 3 — Tuesday
Six lifts fill six days, Monday to Saturday. Lift 3 is Monday and lift 5 is Thursday. Lift 2 is immediately before 5, so Wednesday; lift 1 is immediately after 5, so Friday. The highest number, 6, takes the last day, Saturday. Only Tuesday and lift 4 are left, so lift 4 is Tuesday. ```puzzle:grid cols: Mon, Tue, Wed, Thu, Fri, Sat row: 3, 4, 2, 5, 1, 6 ``` Lift 4 is used on Tuesday. Friday (option 1) belongs to lift 1, Thursday (option 2) to lift 5 and Saturday (option 4) to lift 6.
How many lifts will be used between lift 4 and lift 6? (SI 2 Jul 2023)
- 1Two
- 2Four
- 3Three
- 4One
Show answer
Answer: 3 — Three
Six lifts fill six days, Monday to Saturday. Lift 3 is Monday and lift 5 is Thursday. Lift 2 is immediately before 5, so Wednesday; lift 1 is immediately after 5, so Friday. The highest number, 6, takes the last day, Saturday. Only Tuesday and lift 4 are left, so lift 4 is Tuesday. ```puzzle:grid cols: Mon, Tue, Wed, Thu, Fri, Sat row: 3, 4, 2, 5, 1, 6 ``` Lift 4 is Tuesday and lift 6 is Saturday. Between them lie Wednesday (lift 2), Thursday (lift 5) and Friday (lift 1) — three lifts. Counting the end days themselves would give four (option 2), which is the usual slip.
How many tents will be used between tent 6 and tent 5? (SI 9 Jul 2023)
- 1Three
- 2Four
- 3Two
- 4One
Show answer
Answer: 4 — One
Six days, Monday to Saturday, one tent each. Tent 3 is on the first day, Monday. Tent 2 is on Wednesday, and tent 5 comes immediately after it, so tent 5 is on Thursday. Tent 1 is on the last day, Saturday, which is position 6. 'Only three tents between tents 1 and 6' means three days lie strictly between them, so tent 6 sits at position 6 − 4 = 2, that is Tuesday. The single day left, Friday, must take the only tent left, tent 4. Day · Monday · Tuesday · Wednesday · Thursday · Friday · Saturday Tent · 3 · 6 · 2 · 5 · 4 · 1 Tent 6 is used on Tuesday and tent 5 on Thursday. The only day strictly between them is Wednesday, which carries tent 2, so exactly One tent is used between them. Two is the trap for anyone who counts tents 6 and 5 themselves, or who counts the days inclusively.
How many halls will be used between halls 6 and 5? (SI 15 Jul 2023)
- 1Four
- 2Two
- 3One
- 4Three
Show answer
Answer: 3 — One
Lay the week out. Hall 1 is on the last day, Saturday. Hall 3 is immediately before it, so hall 3 is Friday. Hall 6 is Tuesday, so hall 4, immediately after it, is Wednesday. Four halls between hall 2 and hall 1 means four days separate them, and Saturday minus five days is Monday, so hall 2 is Monday. Only Thursday is left, and only hall 5 is left. Day · Hall Monday · 2 Tuesday · 6 Wednesday · 4 Thursday · 5 Friday · 3 Saturday · 1 Hall 6 is used on Tuesday and hall 5 on Thursday, so only Wednesday — hall 4 — falls between them. That is one hall. 'Two' is the trap for anyone who counts the two days Wednesday and Thursday instead of the halls strictly in between.
On which of the following days will hall 5 be used? (SI 15 Jul 2023)
- 1Thursday
- 2Saturday
- 3Wednesday
- 4Friday
Show answer
Answer: 1 — Thursday
Lay the week out. Hall 1 is on the last day, Saturday. Hall 3 is immediately before it, so hall 3 is Friday. Hall 6 is Tuesday, so hall 4, immediately after it, is Wednesday. Four halls between hall 2 and hall 1 means four days separate them, and Saturday minus five days is Monday, so hall 2 is Monday. Only Thursday is left, and only hall 5 is left. Day · Hall Monday · 2 Tuesday · 6 Wednesday · 4 Thursday · 5 Friday · 3 Saturday · 1 Every other day is claimed — Monday by hall 2, Tuesday by hall 6, Wednesday by hall 4, Friday by hall 3 and Saturday by hall 1 — so hall 5 takes Thursday. Saturday is the trap because it is the 'last day', but that day is explicitly given to hall 1.
Which of these packets will be consumed on Tuesday? (SI 15 Jul 2023)
- 12
- 26
- 34
- 45
Show answer
Answer: 3 — 4
Packet 1 is on Thursday and packet 5 is the day immediately before it, so 5 is on Wednesday. At least two packets lie between 6 and 1. If 6 were on Friday or Saturday only one day could separate it from Thursday, so 6 must be on Monday, leaving Tuesday and Wednesday (two packets) between them. Between 6 (Monday) and 5 (Wednesday) exactly one packet is consumed (Tuesday), so exactly one packet must also lie between 5 (Wednesday) and 3. Counting forward, that puts 3 on Friday with Thursday in between. Only Tuesday and Saturday remain, for packets 2 and 4; packet 4 is not consumed on Saturday, so 4 is on Tuesday and 2 on Saturday. Day · Packet Monday · 6 Tuesday · 4 Wednesday · 5 Thursday · 1 Friday · 3 Saturday · 2 Tuesday carries packet 4. Packet 2 is the trap for anyone who forgets that packet 4 is only barred from Saturday, not from Tuesday.
On which of the following days will packet 3 be consumed? (SI 15 Jul 2023)
- 1Wednesday
- 2Friday
- 3Monday
- 4Saturday
Show answer
Answer: 2 — Friday
Packet 1 is on Thursday and packet 5 is the day immediately before it, so 5 is on Wednesday. At least two packets lie between 6 and 1. If 6 were on Friday or Saturday only one day could separate it from Thursday, so 6 must be on Monday, leaving Tuesday and Wednesday (two packets) between them. Between 6 (Monday) and 5 (Wednesday) exactly one packet is consumed (Tuesday), so exactly one packet must also lie between 5 (Wednesday) and 3. Counting forward, that puts 3 on Friday with Thursday in between. Only Tuesday and Saturday remain, for packets 2 and 4; packet 4 is not consumed on Saturday, so 4 is on Tuesday and 2 on Saturday. Day · Packet Monday · 6 Tuesday · 4 Wednesday · 5 Thursday · 1 Friday · 3 Saturday · 2 Packet 3 falls on Friday. Wednesday is the trap because that day belongs to packet 5, and Monday belongs to packet 6.
How many boxes will be delivered after box 3? (SI 31 Jul 2023)
- 1Four
- 2Three
- 3Two
- 4One
Show answer
Answer: 2 — Three
Box 6 is on Thursday and exactly two boxes fall between box 6 and box 2, so box 2 is three days away from Thursday — Monday (Sunday is not in the week). Box 4 is on Saturday and box 5 immediately before it, so box 5 is on Friday. Box 1 comes immediately after box 2, so box 1 is on Tuesday, and the only day left, Wednesday, goes to box 3. Schedule — Monday: 2, Tuesday: 1, Wednesday: 3, Thursday: 6, Friday: 5, Saturday: 4. Box 3 is on Wednesday, so the boxes delivered after it are box 6 (Thursday), box 5 (Friday) and box 4 (Saturday) — three boxes. Four (option 1) would need box 3 on Tuesday, but Tuesday is box 1's day.
Which of the following boxes will be delivered on Wednesday? (SI 31 Jul 2023)
- 1Box 6
- 2Box 5
- 3Box 2
- 4Box 3
Show answer
Answer: 4 — Box 3
Box 6 is on Thursday and exactly two boxes fall between box 6 and box 2, so box 2 is three days away from Thursday — Monday (Sunday is not in the week). Box 4 is on Saturday and box 5 immediately before it, so box 5 is on Friday. Box 1 comes immediately after box 2, so box 1 is on Tuesday, and the only day left, Wednesday, goes to box 3. Schedule — Monday: 2, Tuesday: 1, Wednesday: 3, Thursday: 6, Friday: 5, Saturday: 4. Wednesday is the one day not claimed by boxes 2, 1, 6, 5 and 4, so box 3 is delivered on Wednesday. Box 2 (option 3) is on Monday, three days before box 6's Thursday.
Part 3 · Grids and value puzzles — 8 questions
Two or three attributes per person, and a table to hold them
A grid puzzle gives several people and two or more attributes each — a sport and a colour, a post and a colour, a date and a destination. One ordered column is no longer enough, so draw a table: one row per person, one column per attribute. Fill in only what a clue states outright, and leave the rest blank rather than guessing. Then use the clues that eliminate: the DGP likes pink plus Anil is the DGP fills two cells at once. When a column has only one empty cell left, the remaining value goes there with no further reasoning. Four more questions in this group are not arrangements at all. They give ages or marks as relations — P's age is one-fourth of V's, short answers plus multiple choice carry 80 marks — and the answer is arithmetic. Read what is asked before computing everything: several of these need only two of the six people.
The four grid puzzles, solved (4)Tap to open
Six players – P to U – plays six different games among – tennis, badminton, cricket, kabaddi, squash and billiards – but not necessarily in the same order. Neither S nor Q plays badminton. Neither Q nor U plays cricket. R plays squash. Either T or Q plays badminton. P plays either badminton or billiards. Which of the following player-game combination is definitely true? (SI 20 Aug 2021)
- 1U – Tennis
- 2P – Billiards
- 3S – Badminton
- 4Q – Kabaddi
Show answer
Answer: 2 — P – Billiards
Start with badminton. The clue says badminton is played by T or Q, and another clue says Q does not play badminton; so T plays badminton. P was allowed only badminton or billiards, and badminton has now gone to T, so P plays billiards — that is a forced, definite pairing. R plays squash by the third clue. That leaves tennis, cricket and kabaddi for Q, S and U. Neither Q nor U plays cricket, so S plays cricket, and Q and U take tennis and kabaddi in one order or the other, with nothing in the clues to decide which. So 'U – Tennis' and 'Q – Kabaddi' are possible but not definite, and 'S – Badminton' is impossible twice over — S is barred from badminton and S has been fixed on cricket. The only pairing that must be true is P – Billiards.
There are seven persons, namely Annu, Anil, Amita, Ankit, Amit, Anita and Ankita. They like different types of colours from blue, red, white, black, pink, yellow and orange, but not necessarily in the same order. Each of them has a different profession, namely DM, SP, SO, CO, DGP, SSP and SI but not necessarily in the same order. Annu does not like orange colour. The SP likes blue colour. Amita and Anita like blue and yellow, though not necessarily in that order. Anil is a DGP. The person who likes orange colour is an SI. The SO and the DGP like white and pink colour, though not necessarily in the same order. Anita is an SSP. The one who likes pink colour, is a DGP. Ankita who likes black colour, is not an SSP. Annu is not an SI. Amit, a DM, like red colour. The CO likes black colour. The one who likes white colour is an SO. Which of the following statements is true? (SI 16 Oct 2022)
- 1SO likes black colour
- 2Amita is an SSP
- 3SI likes orange colour
- 4One who likes black colour is a SO
Show answer
Answer: 3 — SI likes orange colour
Fix the certain links first: Amit = DM = red; Anil = DGP, and the DGP likes pink, so Anil = pink. Anita = SSP; Amita and Anita hold blue and yellow, and the SP likes blue, so Anita (already SSP) must take yellow and Amita takes blue, which makes Amita the SP. Ankita = black, and the CO likes black, so Ankita = CO (consistent with 'Ankita is not an SSP'). White belongs to the SO; the only people left are Annu and Ankit, and the leftover colours are white and orange. Annu is neither orange nor SI, so Annu = white = SO and Ankit = orange = SI. Full solution (unique): Amit–red–DM, Anil–pink–DGP, Amita–blue–SP, Anita–yellow–SSP, Ankita–black–CO, Annu–white–SO, Ankit–orange–SI. Now test the options: the SO (Annu) likes white, not black, so 1 is false; Amita is the SP, not the SSP, so 2 is false; the person who likes black (Ankita) is the CO, not the SO, so 4 is false — 4 is the tempting one because it merely swaps the wording of 1. The SI (Ankit) does like orange, so 3 is true.
Six people P, Q, R, S, T and U leave Delhi on six different dates of August 2020 out of 10, 12, 16, 21, 25 and 29, but not necessarily in that order. There are three dates between the departure dates of S and U. Only one person leaves between the departure dates of T and U. Q leaves immediately after P but is not the last person to leave. T is neither the first nor the last person to leave. Neither U nor S is the last person to leave. How many people leave between the departures of S and R? (SI 19 Aug 2021)
- 1Three
- 2One
- 3Two
- 4Four
Show answer
Answer: 2 — One
The clue 'three dates between the departure dates of S and U' is about the calendar, not about the seats: it is satisfied only when the two dates are four days apart, so that exactly three dates fall between them. Among 10, 12, 16, 21, 25 and 29 the pairs four days apart are (12, 16), (21, 25) and (25, 29). Now use the rest. T and U have exactly one person between them, so they sit two places apart in the order. Q is immediately after P, Q is not last, T is neither first nor last, and neither U nor S is last — so R is the last to leave, on 29. That kills the pair (25, 29) for S and U. Trying (12, 16) leaves no room for the consecutive block P, Q; trying S = 21 and U = 25 works: T must be two places before U, i.e. on 16, and the block P, Q then takes 10 and 12. The order is therefore P (10), Q (12), T (16), S (21), U (25), R (29). Between S on 21 and R on 29 only U leaves, on 25 — exactly one person. The tempting wrong answer is 'two' (option 3), got by counting the two dates 25 and 29 instead of the people strictly between them.
In a week, six lectures are scheduled in such a way that the first lecture is on Monday and the last is on Sunday. IT lecture is not on Tuesday or Saturday. History lecture is immediately after the lecture of physics. Civics lecture is not on Sunday, and there is a one-day gap between the lectures of civics and biology. One day prior to the schedule of math lecture, there is no lecture (as that day is the 'off' day, and Sunday is not the 'off' day). Biology lecture is on Friday. Which of the following is the off day? (SI 18 Aug 2021)
- 1Wednesday
- 2Saturday
- 3Tuesday
- 4Friday
Show answer
Answer: 2 — Saturday
Seven days carry six lectures, so exactly one day is free, and Monday and Sunday are taken by the first and last lectures. Start from the fixed point: biology is on Friday. A one-day gap from biology means civics sits on Wednesday or Sunday, and civics is barred from Sunday, so civics is on Wednesday. The off day must be the day immediately before the maths lecture, and it cannot be Monday or Sunday (both carry lectures) nor Wednesday or Friday (civics and biology), which leaves Tuesday, Thursday or Saturday. If the off day were Tuesday, maths would be on Wednesday, which is civics; if it were Thursday, maths would be on Friday, which is biology. Only Saturday works, putting maths on Sunday. Day · Lecture Monday · Physics Tuesday · History Wednesday · Civics Thursday · IT Friday · Biology Saturday · off Sunday · Maths The remaining three days Monday, Tuesday and Thursday take IT, physics and history; since history must follow physics immediately, they occupy Monday and Tuesday, leaving IT on Thursday, which also satisfies the bar on IT falling on Tuesday or Saturday. Every clue is met, and the off day is Saturday.
The four value puzzles, solved (4)Tap to open
In the number 9654032718, if the first digit is interchanged with the last digit, the second digit with the second-last digit, and so on with the remaining digits, how many digits will remain in the same position? (SI 2 Jul 2023)
- 10
- 25
- 34
- 43
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Answer: 1 — 0
The operation simply reverses the number, so a digit keeps its position only if it equals the digit mirrored across the centre. With ten digits there are five mirror pairs. 9 6 5 4 0 3 2 7 1 8 - 1st and 10th: 9 and 8 — different - 2nd and 9th: 6 and 1 — different - 3rd and 8th: 5 and 7 — different - 4th and 7th: 4 and 2 — different - 5th and 6th: 0 and 3 — different No pair matches, so 0 digits stay put. (The number has an even count of digits, so there is no fixed middle digit either — that is the trap behind the non-zero options.)
P, Q, R, S, T and U are selected for a university admission interview according to the marks obtained in the admission test. The test was of 140 marks in total, comprising 40 marks for multiple-choice questions, 40 marks for short-answer questions and 60 marks for long-answer questions. R got full marks for the multiple-choice questions, half marks for the short-answer questions, and for the long-answer questions obtained 30% of the marks P obtained. T and U each obtained 50% of the combined total marks of the short-answer and multiple-choice questions. S obtained 10 marks more than T and U in the short-answer and multiple-choice questions. T, U and S each obtained 50 marks in the long-answer questions. P obtained 10% more marks than U in the long-answer questions and obtained 60 marks in total in the short-answer and multiple-choice questions. Q obtained 20 marks less than P. Who obtained the highest marks? (SI 21 Jun 2023)
- 1Q
- 2T
- 3S
- 4P
Show answer
Answer: 4 — P
Short-answer plus multiple-choice together carry 40 + 40 = 80 marks; long answers carry 60. T and U: 50% of 80 = 40 in the objective part, plus 50 in long answers → 90 each. S: 10 more than T and U in the objective part = 50, plus 50 in long answers → 100. P: 60 in the objective part; in long answers P got 10% more than U, i.e. 50 × 1.1 = 55 → 115. R: full 40 in multiple choice, half of 40 = 20 in short answers, and 30% of P's long-answer marks = 0.30 × 55 = 16.5 → 76.5. Q: 20 less than P = 115 − 20 = 95. Ranking the totals: P 115, S 100, Q 95, T 90, U 90, R 76.5. Candidate · Objective (MCQ + short) · Long answer · Total P · 60 · 55 · 115 S · 50 · 50 · 100 Q · — · — · 95 T · 40 · 50 · 90 U · 40 · 50 · 90 R · 60 · 16.5 · 76.5 S (option 3) is the trap, since S beats T and U in both parts, but P's 55 in long answers puts P ahead.
According to the marks obtained in an entrance examination, P, Q, R, S, T and U are selected for the admission interview at a university. The examination was of 140 marks, comprising multiple-choice questions of 40 marks, short-answer questions of 40 marks and long-answer questions of 60 marks. R obtained full marks in the multiple-choice questions, half the marks in the short-answer questions, and in the long-answer questions 30% of the marks P obtained. T and U obtained 50% of the total marks of the short-answer and multiple-choice questions. S obtained 10 marks more than T and U in the short-answer and multiple-choice questions. T, U and S each obtained 50 marks in the long-answer questions, and P obtained 10% more marks than U in the long-answer questions and a total of 60 marks in the short-answer and multiple-choice questions. Q scored 20 marks less than P. What is the difference between the marks of P and R? (SI 15 Jul 2023)
- 125.5
- 238.5
- 3115
- 465.5
Show answer
Answer: 2 — 38.5
Only P and R are needed. P: long answers = 10% more than U's 50 = 55. Short + MCQ = 60 (given). P total = 55 + 60 = 115. R: MCQ full = 40; short answers half of 40 = 20; long answers = 30% of P's long-answer score = 0.30 × 55 = 16.5. R total = 40 + 20 + 16.5 = 76.5. Difference = 115 − 76.5 = 38.5. The trap is taking R's 30% of P's total (0.30 × 115 = 34.5, giving 25.5) — the clue ties it to the long-answer marks only.
There are 6 people, P, V, S, T, U and F. P’s age is one-fourth of V’s age. U’s age is 16. S’s age is one-sixth of F’s age, and F’s age will be twice the age of V after 10 years. V’s 8th birthday was celebrated 2 years ago. What is the difference between U’s age and V’s age? (SI 29 Jul 2023)
- 14
- 23
- 31
- 46
Show answer
Answer: 4 — 6
The question asks only for U and V, so only two clues matter. U's age is given directly: U = 16. V's 8th birthday was celebrated 2 years ago, so V was 8 two years ago and V = 8 + 2 = 10 now. Difference = 16 − 10 = 6. The clues about P, S, T and F are deliberate padding: they fix F = 30 and S = 5 (since F + 10 = 2 × (10 + 10) = 40), and P = 10/4 = 2.5, none of which is needed. Candidates who chase F first waste the time and often land on 4 (option 1).
Part 4 · The exam-hall routine
Number first, guess never
- Count the slots
- Fix the direction
- Place the exact clues
- Answer both questions
- Numbering from the bottom and then reading a clue from the top. Write the direction beside the column and check each clue against it.
- Reading “four between” as four apart. It is five apart. Count the gap, then add one.
- Forgetting the free day. Six items over seven days leaves one day empty, and which day it is is often the whole answer.
- Filling a grid cell on a hunch. Leave it blank. A later clue will fill it, and a wrong guess poisons every cell after it.
- Computing every value when only two are asked. In the age and marks puzzles, read the question before the clues.
- Draw the slots before reading the clues twice.
- Decide once: 1 = bottom, or 1 = top.
- k between → slot numbers differ by k + 1.
- Days are just slots 1 to 6 or 1 to 7.
- Six items, seven days → one day is free.
- Two attributes each → draw a table, not a line.
- One empty cell in a column → it fills itself.
- Never write a cell you have only guessed.
- Ages and marks puzzles: read the question first.
- One puzzle, two questions. Keep the sketch.