Clock Hands

The round hands you an angle — 61.5°, 137°, 7.5° — and a blank dial sitting at twelve. Your job is to move the hands until they are exactly that far apart. There is no dragging and no eyeballing: you pick an hour, then the tens and the units of the minutes, and press check. A round is over in a couple of minutes, and the whole thing rests on one fact you can carry out of it — the minute hand gains 5.5° on the hour hand every minute, so the gap you want is only ever a division away. Every angle apart from 0° and 180° is made twice on a twelve-hour dial, and either time counts.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Read the target. The gauge on the right draws the angle you are aiming at and the status row prints it. The dial on the left shows what you currently have set, starting at 12:00 with both hands together.
3. Move along a row with Left and Right, and change row with Up and Down. There are three rows: the hour, the tens of the minutes, and the units of the minutes.
4. Put a value on the dial with Enter, or press the tile with the pointer. The tile you set says "set" underneath its number and the dial redraws immediately. Setting values is free — you can move the hands around as much as you like.
5. Check the time with F or Shift, or press the Check this time button. Only a check costs anything.
6. Read the answer back. A wrong check tells you the angle your time actually made and how far that is from the target, and whether the hour you tried holds an answer at all. Every check you have made stays on screen underneath, so you are reasoning from a table rather than from memory.
7. Win when the hands on your time are exactly the target angle apart. The round ends when the checks run out, and then the board shows both times that would have worked and the arithmetic for one of them.

How many checks you get comes from how long the game's own solver had to search before it found the first answer: a target answered in the twelve o'clock hour is tight and worth less, one whose answers hide at ten or eleven is more forgiving and pays more.

How do I find the time when the clock hands are a given angle apart?

Work from the hour. At h o'clock the minute hand is on twelve and the hour hand is 30h degrees ahead of it — 120° at four o'clock, 210° at seven. From that instant the minute hand turns 6° a minute and the hour hand only 0.5°, so the minute hand closes 5.5° every minute. After t minutes the gap has changed by 5.5t, which gives the whole method in one line:

t = (30h ± A) ÷ 5.5

Take the hour you are guessing, add the target angle A for the case where the minute hand has swung past the hour hand and subtract it for the case where it is still short, divide by 5.5, and you have the minutes. If the division does not come out to a whole number of minutes, or lands outside 0 to 59, that hour has no answer and you move to the next one. Worked example: 61.5° at four o'clock gives (120 + 61.5) ÷ 5.5 = 33 exactly, so 4:33 is one answer; (120 − 61.5) ÷ 5.5 = 10.63…, which is not a whole minute, so the other side of that hour has nothing.

Why are there always two answers?

Because the gap opens, reaches half a turn, and then closes again. Measured clockwise from the hour hand, the minute hand's lead runs all the way from 0° to 360° over the twelve hours, and an angle of, say, 61.5° is reached once on the way out (lead 61.5°) and once coming back (lead 298.5°, which is the same 61.5° looked at from the other side). Only 0° and 180° escape this, because they sit exactly at the two turning points — 0° happens once, at 12:00, and 180° happens once, at 6:00. Those two are the only angles with a single answer, which is exactly why the game never deals them: with them out of the draw, "there are two answers and either counts" holds every single round.

Is every target actually reachable?

Yes, by construction rather than by hope. The round draws a time first, from the 718 whole-minute readings that are neither 12:00 nor 6:00, and then asks for the angle that time makes. The drawn time is an answer before the question exists, so there is no rejection loop anywhere that could stall and no way to be handed something impossible. The board then re-derives the full answer set with a separate routine that walks all 720 whole minutes of the dial and keeps every reading whose measured angle matches — that routine never sees the drawn time, so the guarantee is verified rather than assumed, and it is what decides which times the check accepts.

Why does the game work in halves of a degree?

Because clock angles genuinely are half-degrees, and rounding them is how this puzzle usually goes wrong. The hour hand moves 0.5° a minute, so 3:15 is 7.5° and 4:33 is 61.5°; a version that reports whole degrees has to round, and once it rounds it starts refusing correct answers and showing two different times as the same figure. Everything here is held as a whole number of half-degrees internally — a full turn is 720 of them — so nothing is ever a rounded fraction, the check can tell you that you are 5.5° too wide rather than "wrong", and the same puzzle plays out identically on every device.

Is there any money, betting or in-app purchase in this?

None, and there never will be. There is nothing to buy, no currency of any kind, no gambling mechanic, and no way to spend anything on a better outcome. The score exists so that a reasoned answer feels better than a lucky one, and it is not for sale. The game is a clock face and some arithmetic.

Can I play it with a keyboard or a screen reader?

Both. Left and Right move along a row, Up and Down change row, Enter puts the value under the cursor on the dial, and F or Shift checks the time. Every tile announces what it stands for in words — "4 o'clock", "30 to 39 minutes past", "3 minutes on top of the tens" — and whether it is currently on the dial. The board announces the target angle, the time you have set, how many checks are left, and what your last check actually made. The dial itself is a picture and is hidden from screen readers, because every number on it is already in the text; its two hands are told apart by length and thickness rather than by colour, and a set tile carries the word "set" as well as a ring.

Does it work offline?

Yes. Once the page has loaded once, the whole game is on your device — the generator, the solver, the rules and this page. Nothing is fetched while you play and no result leaves the device.

A twelve-hour dial and whole minutes only, which is 720 readings and 361 possible angles from 0° to 180° in half-degree steps. Seconds are not modelled; a target is always reachable by a whole number of minutes, because the round is built from one. Twelve o'clock and six o'clock never come up as targets, so every round has exactly two answers. Checks run from three to six, derived from how far the game's own search had to go, and a check that repeats a time you have already tried costs the same as a fresh one — the budget is a hard limit on how many times a round can be checked, not a politeness. There is no hint button and no partial credit: the hands are the target angle apart or they are not.

Target 24 is the other arithmetic-search game here — a fixed set of numbers and a fixed answer, with the search over the operations rather than over the dial. Weight Split and Cut Share both ask you to hit an exact total rather than an exact angle, and both count how many answers exist before you start, the way this one counts its two. Gap Logic is the same shape of puzzle with the arithmetic taken out: a set of constraints, one arrangement that fits, and a budget that stops you shuffling your way there.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.