Watch

Post guards inside a building so that every room is being watched, using as few of them as possible. The smallest number needed turns out to equal the largest set of corridors that share no room, which is a proven result and a useful hint.

How to play

The circles are rooms, laid out in two wings, and the lines between them are corridors.

  1. Start with the busiest rooms A room with five corridors is nearly always worth a guard. One with a single corridor almost never is.
  2. Look for forced rooms If a room has a corridor to a room with nothing else, the busy end is the one to guard.
  3. Count the independent corridors Find corridors that share no room between them. Each needs its own guard, so that count is a floor — and it is also the answer.
Full instructions

In depth

Covering Every Corridor with the Fewest Guards

This article explains the rules, controls, and strategies for Watch, a guard-placement puzzle where every corridor must be overlooked and the fewest guards that can do it equals the largest set of corridors that share no room.

Screenshot: How to play Watch
How to play Watch as it appears when the page opens.

What the game is about

You are given a building plan drawn as circles and lines. Each circle is a room. Each line is a corridor connecting two rooms. The rooms are divided into two wings, left and right, and every corridor runs between the wings, never within one. Tap a room to post a guard there. A corridor counts as watched if at least one of the two rooms at its ends has a guard. Your goal is to make every corridor watched while using as few guards as possible.

The game tells you the fewest guards that can cover every corridor. Your job is to find an arrangement that reaches that number. Any valid set of rooms that watches everything and matches the target count is accepted. There is often more than one correct answer.

Rules in detail

A guard posted in a room watches every corridor that touches that room. If a room has five corridors, one guard there covers all five. A guard does not watch corridors two rooms away or corridors in rooms nearby but not directly connected. Only the corridors that touch the guard's own room are covered.

You can post a guard by tapping a room. Tap the same room again to stand that guard down. There is no cost to posting or removing guards. Only the count of guards in place when every corridor is green matters. The game does not track how many times you changed your mind.

Controls

On any device, tap or click a room circle to toggle a guard on or off. Corridors turn green when watched. The scoreboard above the board shows three figures: Corridors watched (how many of the total are currently covered), Guards posted (how many rooms you have staffed), and Fewest guards (the target number you are trying to match). The Building dropdown offers Small, Medium, and Large. The New game button generates a fresh building.

How scoring works

Your score is the number of guards you use when every corridor is watched. Lower is better. If you cover everything with exactly the target count, you win. If you cover everything with more guards than the target, the game tells you the number is too high and prompts you to stand one down. The puzzle is not finished until you match the target.

The game tracks your personal best across sessions. Since all buildings at the same difficulty have roughly the same target count, improving your best usually means solving faster rather than with fewer guards, but the stored number is the guard count itself.

Starting with the busiest rooms

The most reliable opening strategy is to look at which rooms have the most corridors. A room with five corridors covers five lines with a single guard. A room with one corridor covers only one. If every corridor from a high-degree room also touches a low-degree room on the other side, guarding the busy room is almost always better.

After guarding the busiest rooms, look at which corridors are still dark. If a dark corridor connects a room with only one other corridor, the room at the other end of that corridor is the one to guard. This cascading logic often fills in most of the answer before you need to think harder.

Finding forced rooms

A forced room is one that must be guarded in any optimal solution. The simplest case is a room on one side whose only corridor leads to a room on the other side that has many corridors. Guarding the busy end covers that corridor plus several others. Guarding the quiet end covers only one. No optimal solution picks the quiet end when the busy end is available.

Another forced case appears when a room is the only path to cover a particular corridor. If a corridor connects room A on the left to room B on the right, and room B has no other corridors, then either A or B must be guarded. If A has four other corridors, guarding A is strictly better. Spotting these forced choices before you start tapping saves a lot of trial and error.

Counting independent corridors

The deepest strategy in Watch comes from flipping the question. Instead of asking which rooms to guard, ask how many corridors you can pick that share no room between them. Each of those corridors needs its own guard, because no single guard can cover two corridors that do not share a room. That count is a hard floor on the number of guards you need.

The remarkable thing, and the reason the puzzle always has a clean answer, is that in a building with two wings the floor is also the ceiling. You never need more guards than that count. This equality is a mathematical result proved in 1931, and the game checks it on every board before offering it to you. If you can find the independent corridors, you know the answer immediately.

Trimming excess guards

Once every corridor is green, you may have used more guards than necessary. The simplest way to trim is to try removing each guard in turn. If removing a guard leaves every corridor still watched, that guard was spare. Remove it and move on to the next. This brute-force check works well on Small buildings. On Medium and Large buildings, it helps to start by removing guards in the least-connected rooms first, since those are the most likely to be redundant.

If removing any single guard breaks the coverage, but you are still above the target, then two guards need to be moved, not just one removed. Try standing down a guard and posting one in a different room that covers the same corridors plus one more.

A useful habit is to trim from the edges inward. Rooms with only one corridor are rarely the right place for a guard, so if you have one posted there, it was probably a leftover from experimenting. Stand it down and see if the room at the other end of its corridor already has a guard covering it.

Common beginner mistakes

The most common mistake is guarding the quiet end of a corridor instead of the busy end. If a corridor connects a room with one corridor to a room with four, guarding the one-corridor room wastes a guard that covers nothing else.

  • Guarding every room on one side. This always works but always uses too many guards. The target is usually much smaller than the number of rooms in either wing.
  • Ignoring rooms with a single corridor. These rooms still need their one corridor watched, so the room at the other end must be covered.
  • Giving up when you are one guard over the target. Try standing each guard down in turn. Often one of them is redundant and you did not notice because all corridors stayed green.
  • Not reading the fewest-guards number. It is displayed above the board and tells you exactly how many you need.
  • Posting guards on the same side of the building. Since every corridor runs between the two wings, a guard on the left covers corridors going right and a guard on the right covers corridors going left. Clustering all your guards in one wing often leaves corridors on the far side uncovered.

Difficulty levels

Small buildings have four rooms in each wing and seven corridors. The target is usually three guards. These boards are small enough that you can try every combination by hand. Medium buildings have five rooms in each wing and ten corridors. The target is typically three to four guards, and the number of possible combinations is large enough that trial and error is slow. Large buildings have six rooms per wing and thirteen corridors. The target can reach five guards, and the graph is complex enough that the independent-corridor strategy becomes essential.

Every building is generated fresh and checked with an exhaustive search. The game also verifies the equality between the fewest guards and the largest set of independent corridors. If a generated building fails either check, it is discarded and a new one is built.

Privacy and your device

The entire game runs in your browser. No data is sent anywhere, no account is needed, and your best score is stored in local browser storage on this device only. Once the page has loaded, the game works fully offline.

Help

How to play Watch

The circles are rooms, laid out in two wings, and the lines between them are corridors. Tap a room to post a guard and tap again to stand them down; a corridor turns green as soon as there is a guard at either end of it. Every corridor has to be green, and the number of guards you used is your score.

Start with the busiest rooms

A room with five corridors is nearly always worth a guard. One with a single corridor almost never is.

Look for forced rooms

If a room has a corridor to a room with nothing else, the busy end is the one to guard.

Count the independent corridors

Find corridors that share no room between them. Each needs its own guard, so that count is a floor — and it is also the answer.

Try standing one down

Once everything is watched, remove each guard in turn. If nothing goes dark, that guard was spare.

Kőnig’s theorem

Two questions about a network with two sides look quite different. How few points can you choose so that every line touches one of them? And how many lines can you choose so that no two of them share a point? The first is a covering question, the second a matching question, and in 1931 Dénes Kőnig proved that in a two-sided network they always have the same answer. One direction is easy: lines that share no point need a point each, so the cover can never be smaller than the matching. The other direction is the theorem, and it is why this problem is easy here and hard in general — for networks that are not two-sided, finding the smallest cover is NP-complete, one of Karp’s original twenty-one. Every building here is searched completely, and the game checks Kőnig’s equality on the board before offering it to you.

Good to know

One guard per independent corridor

Corridors sharing no room cannot share a guard, so they set the minimum immediately.

And that minimum is achievable

In a building of two wings, you never need more guards than that count. That is the surprising half.

Guards watch rooms, not corridors

A guard covers every corridor touching their room, which is why the busy rooms are worth so much.

Standing down is free

Only the guards posted when everything is watched are counted.

Common questions

Can a corridor run within one wing?
No, and that is what makes the answer exact. Kőnig’s theorem needs the two-sided shape.
Does a guard watch corridors further away?
No. Only the corridors touching their own room.
Is there only one best arrangement?
Often not. Any set of the right size that watches everything wins.
Would this be hard in a normal building?
Very. Without the two wings it is one of the classic hard problems.
Is the fewest-guards figure exact?
Yes, twice over — searched exhaustively, and cross-checked against the matching.