Puzzle: You awaken in a dimly lit room, the door in front of you sealed tight with an electronic lock requesting a 4-digit code. On the wall, there’s a note scribbled hastily:
"Within these walls lies the secret to escape.
Nine digits, each used once, assemble your fate.
Numbers alone won’t free your soul,
Reveal their meaning, find the whole.
Look upon the symbols beneath the note:
- A clock showing the time: 3:15
- A painting of a triangle with angles marked: 70°, 50°, ?°
- A book titled “Prime Mysteries” open to a page highlighting these numbers: 2, 3, 5, 7, 11, 13
- A calendar page flipped to March 7th, with the number “21” circled in red.
Engraved on the door is a cryptic phrase:
"Find the missing angle, unlock primes, note the hour’s hand, then add the special date."
Remember, numbers 1 through 9 are used only once in the code.
What is the 4-digit code that will unlock the door?
Solution:
Step 1: Find the missing angle of the triangle.
The sum of angles in a triangle is 180°. Given 70° and 50°, the missing angle is:
180° - (70° + 50°) = 180° - 120° = 60°
Step 2: Unlock the primes.
The note references primes (2,3,5,7,11,13). The first four single-digit primes are 2, 3, 5, and 7. Since numbers can only be used once, and we need four digits total, the primes clue likely points us toward one specific prime to use.
Also, the phrase “unlock primes” could refer to the smallest prime in the list that hasn’t been used yet, or a prime directly related to the other clues.
Step 3: Note the hour’s hand.
The clock shows 3:15. The hour hand at 3:15 is not exactly on 3; it has moved a quarter of the way toward 4. Each hour represents 30°, so the hour hand at 3:15 is at:
3 hours × 30° + 15 minutes × 0.5° per minute = 90° + 7.5° = 97.5°
The hour hand’s position is 97.5°, but since numbers are from 1-9 and used only once, this might indicate the digit 9 (from 97.5) or 7 (from 7.5).
Alternatively, it might suggest the digit 3 (the hour) or 1 and 5 (minutes).
Step 4: Add the special date “21.”
The calendar page shows March 7th and “21” circled. It might mean 3/7 → 3 and 7 digits or 21 as a digit (2 and 1) to consider.
Step 5: Deriving the code using unique digits 1-9 only once.
Let’s sum up what we have:
- Missing angle: 60
- The primes: 2,3,5,7,11,13 (only single-digit primes: 2,3,5,7)
- Hour hand (focus on integer digits): 9 or 7
- Special date: 21 → digits 2 and 1
We have digits 1,2,3,5,7,9,6 (from 60) that could be used.
The puzzle says: “Find the missing angle, unlock primes, note the hour’s hand, then add the special date.”
A logical way is to take:
- The missing angle digit(s): 6 and 0 → 6
(0 can’t be used because codes are from 1-9 digits only once, so just the 6) - Unlock prime: smallest prime used, 5 (or 7)
- Hour’s hand digit: 9 (from 97.5°)
- Special date digits: 2 and 1
We need a 4-digit code, digits 1-9 no repeats.
Try this code:
1) The missing angle (6)
2) One prime digit (7)
3) Hour’s hand digit (3—since 3 is the hour shown prominently)
4) Special date’s day digit (1—March 7th, take 1 from “21” or just the digit 1)
Or aligning with the phrase:
- Missing angle: 60 → take 6
- Unlock primes: pick the prime digit 5 (from the "Prime Mysteries")
- Hour’s hand: 3 (hour is 3)
- Special date: 7 (March 7th)
Digits: 6,5,3,7 (all between 1-9, no repeats)
Code: 6537
Verification:
- Digits 6,5,3,7 all unique and between 1-9
- Based on all clues given:
- 6 from missing angle (60) as 0 is invalid
- 5 from prime numbers
- 3 from hour on the clock
- 7 from calendar date (March 7)
Door unlocks with code 6537.
Hints:
- Remember that the sum of angles in a triangle is always 180° — find the missing angle first.
- The prime numbers highlighted should help you select a digit that fits uniquely without repetition.
- The time on the clock and the date on the calendar both give you digits to include in the code. Use these clues carefully!
Inputs used
Story-Based Puzzle Generator
Generate challenging and themed puzzles from scratch by simply providing the type, theme, difficulty, and your desired constraints. Perfect for game designers, educators, or puzzle lovers looking to add creative challenges to their content. Includes the puzzle, full solution, and up to 5 hints tailored to your setup.
Prompt body