Setting an analog clock to a target time in a "set the clock game" means matching the hour and minute hands on a 12-hour analog dial to a specific time using the continuous hand-rate formulas minuteAngle = 6 × minute and hourAngle = 30 × (hour mod 12) + 0.5 × minute. The minute hand advances six degrees for every minute because a full 360-degree turn covers sixty minutes, and the hour hand advances thirty degrees per hour plus an additional one-half degree for every minute that has elapsed past the hour mark. Set-the-clock puzzles ask the player to combine those two rates and reproduce a named target such as 3:00, 6:30, 9:45, 12:00, or 2:25. A clean deterministic version of this task runs entirely in the browser, draws the dial on a real Canvas, and grades each card for exactly 200 points so that a perfect run reaches 1,000. Once a target is matched, the next card opens with its own target time and the route continues until all five clocks are solved or two distinct wrong settings have been recorded.
What "Set the Clock" Games Actually Ask You to Do
A set the clock game is built around a small loop of analog clocks. Each card displays a target time written in hour-and-minute form, and the player adjusts two controls — an hour value from one through twelve and a minute value that snaps to multiples of five from zero through fifty-five. Both controls update the same model in real time: the digital readout and the Canvas-rendered hands move together, so there is no hidden animation loop and no guessing about what was actually submitted. Submission is explicit; pressing Enter or clicking the submit button compares the selected digital time against the target name on the card and either awards 200 points or records one recoverable error.
The five-card format turns the genre from a single drill into a fixed route with a single correct answer per card and a known maximum score, which is what makes the whole sequence reproducible instead of randomized. That reproducibility is what separates a genuine set the clock puzzle from a randomized drill: the same five target times appear every run in the same order, so a player can study the angle pairs once and replay the route with identical feedback every time.
Why the Hour Hand Moves Between Marks
The reason set the clock games reference both hand angles is that the hour hand on a real analog clock does not sit exactly on a numeral except at the top of each hour. It sweeps continuously at 0.5 degrees per minute, so by 6:30 it has moved thirty minutes past the six mark and points exactly halfway between six and seven. To see this calculation explicitly, take the target 6:30 with minute = 30 and hour = 6:
- minuteAngle = 6 × minute = 6 × 30 = 180 degrees
- hourAngle = 30 × (hour mod 12) + 0.5 × minute = 30 × 6 + 0.5 × 30 = 180 + 15 = 195 degrees
The minute hand therefore points straight down at 180 degrees, and the hour hand sits 195 degrees around the dial — 15 degrees past the six mark, halfway toward seven. Set the clock games that ask for "the angle between the hands" or for "the hour-hand position at a precise minute" depend on this continuous motion. A puzzle that ignored the 0.5-degree-per-minute drift would only accept whole-hour targets, which is why the continuous formula is the standard reference. The University of Cambridge NRICH resource on Clock Face Angles walks through a 20:14 example using exactly the same rate relationship, and an independent Rutgers University Telling Time: Advanced Topics page confirms the six-degree minute-hand and continuous hour-hand relationship.
How to Set All Five Clocks in Clock Time Puzzle
Clock Time Puzzle is the deterministic version of this exercise. It draws the five cards on a Canvas, accepts the same hour-and-minute input every run, and scores each card for exactly 200 points. To finish the route:
- Read the target time printed on the current card. The route begins at 3:00 and the status line shows the named target.
- Adjust the hour up or down using the on-screen hour buttons or the Up and Down Arrow keys. Hours move one at a time across the full one-through-twelve range; values outside 1–12 are atomic no-ops.
- Adjust the minute using the minute buttons or the Left and Right Arrow keys. Each press moves the minute value by exactly five, from 00 through 55, and any value outside that range or off the five-minute grid is rejected atomically.
- Watch the Canvas hands update as the digital time changes. There is no animation loop, so the dial reflects only the selected hour and minute — no drift, no smoothing.
- Press Enter or click Submit to register the selected time. An exact match to the card's target adds 200 points and opens the next card. A different wrong setting records one recoverable error; submitting the same wrong setting a second time is a no-op and does not close the file.
- Repeat for 6:30, 9:45, 12:00, and 2:25 in order. Five exact matches award 200 points each, totalling 1,000.
The Five Target Times and Their Hand Angles
The fixed route asks for five targets in a specific order, and each one has a disclosed minute-angle and hour-angle pair drawn directly from the game's Canvas state. The pairs below are written as minute-angle over hour-angle degrees, which is the same order the status line reports after each submission.
| Card | Target | Minute angle | Hour angle |
|---|---|---|---|
| 1 | 3:00 | 0° | 90° |
| 2 | 6:30 | 180° | 195° |
| 3 | 9:45 | 270° | 292.5° |
| 4 | 12:00 | 0° | 0° |
| 5 | 2:25 | 150° | 72.5° |
The 9:45 and 2:25 entries demonstrate the continuous hour-hand motion in practice. At 9:45 the hour hand has advanced 45 minutes past nine, so it sits 22.5 degrees into the next hour position for a total of 292.5 degrees. At 2:25 it has advanced 25 minutes past two, adding 12.5 degrees to the 60-degree base for 72.5 degrees. Both pairs sit cleanly on the five-minute grid, which is why the minute control can reach them without intermediate steps.
Controls, Errors, and the Restart Rule
Clock Time Puzzle accepts three input paths: the on-screen hour and minute buttons, the keyboard Arrow keys, and the Enter key for submission. The hour control moves by one; the minute control moves by five. The R key restarts the run when focus is outside an editing control. Hours outside one through twelve, minutes outside zero through fifty-five, non-integer values, and minutes not divisible by five are atomic no-ops in the product controls — the value simply does not change, and no error is recorded for that press. The lower-level angle function uses a separate 0–23 hour range for evidence vectors, but the player-facing controls stay strictly inside 1–12.
Error handling is single-slot. Submitting a wrong setting records one recoverable error identified by the current card, hour, and minute. Submitting that identical setting again is a no-op. A second distinct wrong setting closes the clock file and freezes both time adjustment and submission. Restart returns to 12:00 on the first card with a zero score and zero errors, ready to replay the same five-target route. The shared game shell additionally tracks a best score and supplies a Boss Key. Everything runs in the browser; there is no account, alarm, scheduling service, timezone claim, API, model, upload, timer dependency, or new package, and no personal clock history is stored or transmitted.
Why These Hand-Angle Formulas Are Trustworthy
The minute-angle and hour-angle formulas used by Clock Time Puzzle are not invented for the game. They come from the standard 60-minute and 12-hour geometry of an analog dial, which is the same geometry used in school textbooks. The Cambridge NRICH page on Clock Face Angles provides the worked 20:14 example that confirms both rates, and the Rutgers Telling Time: Advanced Topics page independently confirms the six-degree minute-hand and the continuous 0.5-degree-per-minute hour-hand rate.
Independent tests in the product verify nine literal angle pairs and the five target times directly, rather than regenerating expected values from production code, and they cover five-minute wrapping, repeat deduplication, two distinct wrong settings, illegal input, restart, the exact 1,000-point finish, and terminal freezing. The product contract is explicit that this is educational entertainment rather than a standardized teaching assessment or a guarantee of mastery: the cited sources support only the mathematical hand rates, and the source comparison is limited to disclosed geometry without validating gameplay itself.