Puzzle

Six or seven boxes are kept one above another, five or six clues are given, and the question asks one of three things: how many boxes are between X and Y, which box is at a given place (for example, third from the top), or which box is directly above or below a given box. This is the most repeated puzzle of the recent Railway papers, and it is only a line of positions.

Think of a lift shaft with places numbered 1 to n from the bottom. Every clue speaks about places, so your whole job is to turn each clue into a number. The exam uses a fixed vocabulary, and each phrase has exactly one meaning:

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Look at six boxes A to F in the picture. C is at the bottom (1) and E at the top (6). F, A and D are kept one over the other, F lowest and D highest, so they are three consecutive places: 2-3-4 or 3-4-5. B is above A with exactly one box between A and B. If F, A, D sat at 3-4-5, then A would be at 4 and B at 6, but 6 is E's place. So the block sits at 2-3-4 and B is at 5, with D between A and B. Notice that the glued block was moved as one object.

The order of work is always the same. First the anchors: "no box above", "only … above / below", top and bottom. Then glued pairs and blocks. Then gap pairs. Then the "somewhere above / below" clues, which only test a placement. The last box goes by elimination. If a gap pair has two or more possible places, list them and let the other clues kill the extras. A box cannot be pushed beyond place n, so a gap that runs off the stack is impossible. At the end write the finished line from bottom to top and read every clue once against it.

Seven persons have exams on the seven days of a week, or five persons travel on the 2nd, 4th, 6th, 8th and 10th of a month, or five friends have birthdays in five different months. The question asks who is on a given day, date or month, or how many persons are between two of them. In the 2026 papers the "dates of a month" form with four or five persons is very common.

The logic is simple: this is the box puzzle lying on its side. Day names, dates and months are only labels on a line of equally spaced places. So convert the labels into slots 1, 2, 3, … at the very start. Monday to Sunday become 1 to 7. The dates 2, 4, 6, 8, 10 become slots 1 to 5, and then "two slots after" means two steps along the line, which is four dates. Every clue now has a fixed meaning:

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In the picture the dates are the top row and the slots are the green numbers below. "Two slots after the person on the 4th" is slot 2 + 2 = slot 4, which is the 8th. When the dates are not a week apart (2, 4, 6 …), never say "one week before"; use the slots. When the dates are 4, 11, 18, 25, "exactly one week before" is simply the previous slot.

The order of work is the whole method. Place exact slots first. Then glued pairs. Then fixed gaps. Then the "before / after" clues and the crosses. The last open slot is filled by elimination. Before testing any option, count the free slots: if two slots are free and two names are left, the puzzle is nearly over. A gap of k persons between means slots differ by k + 1, and the two end persons are never counted as "between". The week does not wrap from Sunday to Monday unless the question says it repeats.

When the labels are months a new filter appears: "Tanvi's month has 30 days". April, June, September and November have 30 days; January, March, May, July, August, October and December have 31; February has 28, or 29 in a leap year (a year divisible by 4, and a century year only if divisible by 400). Write the allowed months beside each name first, then use the glued and order clues. If a glued pair leaves two cases, draw both and let the other clues kill one. After the first working case, test the others too: the answer must be the same in every surviving case.

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Six people (sometimes eight) live on different floors of a building, with floor 1 at the bottom. The clues are positions ("immediately above", "only two people between") and number clues ("an even-numbered floor", "a prime-numbered floor", "the sum of the floors of F and C is 7", "neither even nor prime"). The question asks who lives on a given floor, or how many live above or between. The harder form puts two flats on every floor.

When there is one person per floor, this is exactly the box puzzle: a line of places 1 to n, so the same order of work applies (anchors, glued pairs, gaps, order). The only new thing is the number clues. They do not place a person; they hand you a short list of possible floors, and that list should be written beside the person before you read the next clue. Keep this table in your head for floors 1 to 8:

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Remember two facts: 1 is not a prime number, and 2 is the only even prime. "Neither X nor Y" is two crosses at once, not one. A sum clue is a filter too: for six floors, a sum of 3 can only be (1, 2); a sum of 11 only (5, 6); a sum of 7 is (1, 6), (2, 5) or (3, 4), and then the even or prime clue chooses one pair.

Two flats on each floor. Draw the building as a table: floors are the rows (top row = top floor) and the two flats are the columns (flat 1 on the west, flat 2 on the east). Two phrases must never be mixed. "Lives with / on the same floor as" means the same row. "Lives in the flat directly above / below" means the same column, one floor away.

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In the picture L is on the top floor in flat 2; K is on the same floor (same row); M is directly below L (same column, floor 2); N is on M's floor; O is directly below N (floor 1, flat 1); Q takes the last place. Fix the person with a firm floor and flat first, then fill by rows and columns. Same row means same floor; same column means same flat. "Lives with" is not "same flat". After the last placement, say each clue aloud against the finished building.

A short story gives four to seven persons and one or two lists of things, such as colours, subjects, games or professions, and says who has what: "Neha plays Tennis", "Radhika plays neither Cricket nor Hockey", "Either Aravind or Sunil is the doctor". The question asks one person's value, or which pair is correct, or (in the family form) how one professional is related to another. In the 2026 Steno papers one seven-person story is used for several questions in different shifts, so a fully solved grid pays.

In a linking puzzle every person gets exactly one value of each attribute, nobody shares a value, and no value is left unused. That single fact makes the puzzle solvable, because every tick removes many possibilities. Put the persons in rows and the values in columns. Every clue becomes a tick or a cross:

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Take four friends A, B, C, D and the colours Red, Blue, Green, Yellow. Clues: C likes Red; A likes neither Green nor Yellow; B does not like Green. C gets the Red tick, which crosses Red for A, B and D. A is left with Blue only, so A is Blue. Now read the Green column: A is crossed, B is crossed, C is taken, so D is the only candidate and D gets Green. Yellow is left for B. Notice that D was never mentioned in a clue about Green; the value-wise reading gave it.

Fill by person, then read every column once: a value with a single candidate belongs to that candidate. The double negative "neither … nor" deserves a look of its own. In the second picture P is neither Ap nor Ba, Q neither Ba nor Ma, R neither Ap nor Ma, S neither Ba nor Ma: eight crosses from four sentences. Read the Ba column: P, Q, S are crossed, so R takes Ba. Read the Ma column: Q, R, S are crossed, so P takes Ma. Stop the moment the asked cell is filled.

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The family form. Here the persons are one family and the clues speak in relations: "the Teacher is the mother-in-law of the Pilot's wife", "the Doctor is the husband of the Teacher". Draw the family tree first, couples joined and children below, taking gender from the description and not from the name. Turn each clue into a role and find the only member who fits it; the mother-in-law and father-in-law always belong to the spouse's side. A role that fits one member decides that member at once, and the last profession goes to the last person.

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In a grouping puzzle the persons are not matched with things; they are divided into groups such as cars, benches, houses or teams. Each group has a size limit and often a limit on who may be together: "at least one woman in each car", "a couple does not travel together", "exactly two in each car". The question asks who is with a given person, or which statement is true. A newer form has no names at all: a fixed total of players or students is divided among colours, subjects or clubs, and the clues are only inequalities.

The first thing to do is not to place names, but to count. Counting conditions often fix the shape of the groups before a single name is written. Suppose six people travel in three cars, two in each car, with at least one man and one woman in each car. Two persons per car and one of each kind means exactly one man and one woman in every car. Three women, three cars, at least one woman each: that is exactly one woman per car. Now every clue about a pair becomes a clue about "which woman goes with which man".

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Make the group columns first, write the sizes above them, and place people one by one. Put the certain facts first and keep a "together" clue beside the grid as a hint pair until one of its members gets a group. A family condition such as "members of one family do not share a car" is a cross for every pair of relatives. Counting first, naming later: group sizes and the gender limit usually decide the split before any name is placed. If two arrangements survive, check that the question has the same answer in both.

Count distribution [New Pattern]. Give every group its smallest allowed value, in the stated order, and add. Six players, more Red than Blue, more Blue than Green, at least one Green: Green 1, Blue 2, Red 3. The minimum sum is 6, the same as the total, so there is no spare player and the split is fixed. If the minimum sum equals the total, no group can go above its minimum. If the minimum sum is less than the total, some players are spare; then list the few possible splits, or, for the maximum of the middle group, give the bottom group its minimum and make the top group just one more than the middle. Read the limit words exactly: "at least 2" is 2 or more, "more than" is strictly greater.

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Two kinds of mixed puzzle appear. In the first, persons are divided into groups (rooms, teams, flats) and each person also has an attribute (a drink, a game, a hobby); the clues join the group of one person with the attribute of another. In the second, persons are ranked on two lines at once, for example height and class, or age and rank, with comparison clues such as "O is taller than V but shorter than T"; the question joins the two lines. The way in is the same: split the story into its separate conditions before you fill anything.

Groups with attributes. First identify both conditions and draw the group columns with their sizes and a small list of the attributes. Then notice what the pair clues say about the attributes themselves: if Tea and Milk go together in one room, then Coffee and Juice go together in the other. You have learnt the split of attributes without knowing a single name. Every statement about a person now becomes a statement about a room.

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Fix the group with the most restrictions first, turn each "shares with" clue into a pair that sits in one group, and keep a pair aside as a hint until one of its members is placed. A hint is only a promise that two things end up in the same group; never write it as a certain fact.

Comparison with differences. "A is 4 years older than B", "C is 3 cm shorter than D": nothing is said about A and D, yet the chain joins them. Pick one person as the baseline with value 0 and write everyone as plus (older, taller) or minus (younger, shorter) from him. Order and gaps come out of one list. If a total is given ("the ages add up to 104"), write everyone with one letter and form one equation. A clue with only "older than" and no number gives an order and not a gap, so check that the answer does not depend on the missing value.

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Two lines at once. When height and class are both given, draw two separate lines. Heights run from tallest to shortest, classes from junior to senior (a higher class number is senior). Never put a height clue on the class line. A person is the link between the lines: a clue such as "the third tallest is in class 7" places one person on both. Solve each line as far as it goes, then use the linking clues to join them.

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Here you do not have to arrange anyone. A team or a committee has to be chosen from some people, and a list of conditions says which choices are allowed. The question gives four ready-made choices and asks which one is valid, or which person must be in the committee.

The golden idea: do not construct, test. Take each option and check it against every condition; the option that survives all conditions is the answer. Four kinds of condition appear again and again, and each has an exact test:

Count conditions are the quickest. "The team must have only one teacher", "exactly two women", "a team of five": count the members of that kind in each option and strike out the options that do not match before you read any other condition. Then take the conditions that name one person ("Q cannot be with E, B or C") and scan the survivors for the banned names.

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In the picture, option b passes R1, R2 and R3, while a fails R2, c fails R1 and d fails R3. One failed condition is enough to throw an option away, so strike it out at once and move on. Do not forget to test every condition on the option that passes the first.

"If A then B" and "A only if B" say the same thing: A brings B along. But B does not bring A. Never reverse "if A then B": a team with B but without A is perfectly valid. For the "who must be selected?" form, list all valid teams under the extra condition and pick the person who is present in every one of them.