Clock Tower Christmas Countdown

Once you think you’ve figured out what time the clock was showing before it was tampered with, enter your guess below and help the mechanic set things right in time for the Winterlight Festival.



Look carefully at the clues about the hour and minute hands. Which values are being ruled out for each? Try making two short lists: one for possible hours and one for possible minutes.

Only certain hours are allowed once you apply the rules about prime numbers and perfect squares. Which hour values between 10 PM and 6 AM are both not prime and perfect squares greater than 1? There’s only one.

Now focus on the minute clues. You’ll need to find a number that’s divisible by 5, not prime, not odd, not divisible by the hour, and whose digits add up to something divisible by 3. Only one number fits all of that.

Clue 1: Minute divisible by 5

→ Allows: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Clue 2: Time was changed between 10:00 PM and 6:00 AM

→ Narrows hours to: 10, 11, 12, 1, 2, 3, 4, 5

Clue 3: Hour hand wasn’t on an exact number

→ Excludes any time ending in :00

Clue 4: Neither hour nor minute were prime

→ Excludes prime hours: 2, 3, 5, 11
→ Excludes prime minutes: 5, 25
→ Remaining hours: 1, 4, 10, 12
→ Remaining minutes: 0, 10, 15, 20, 30, 35, 40, 45, 50, 55
→ Further excludes 0 (from Clue 3), and any :00 time

Clue 5: Hour is a perfect square greater than 1

→ Only 4 fits (4 = 2²)

Clue 6: Minute is not odd

→ Excludes 15, 35, 45, 55
→ Remaining: 10, 20, 30, 40, 50

Clue 7: Minutes don’t divide evenly by the hour (4)

→ Excludes: 20 (÷4 = 5), 40 (÷4 = 10)
→ Remaining: 10, 30, 50

Clue 8: Sum of digits of the minute must be divisible by 3

→ 10 = 1, ❌
→ 30 = 3, ✅
→ 50 = 5, ❌

✅ Final answer: 4:30