The Fire Clock

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Long ago in County Kildare, St. Brigid and her friends kept a special fire burning that was never allowed to go out. To ensure the fire was watched day and night, they organized a strict roster.

There were 11 Friends and St. Brigid (12 women in total). They took turns tending the fire in a circle, one person every 24 hours.

Day 1: Friend 1 → Day 2: Friend 2 ... → Day 12: St. Brigid. Then it loops back to Friend 1!

12 St. Brigid 1 Friend 1 2 Friend 2 3 Friend 3 4 Friend 4 5 Friend 5 6 Friend 6 7 Friend 7 8 Friend 8 9 Friend 9 10 Friend 10 11 Friend 11
The Challenge:
Q1 Friend 9 is tending the fire today. Who will be tending the fire 5 days from now?
Q2 The cycle began on Day 1 (Friend 1). Who is tending the fire on Day 50?
Q3 St. Brigid wants to tend the fire on her Feast Day (exactly 100 days from today). If Friend 2 is tending the fire today, will Brigid be on duty? (If not, who?)
Maynooth University Research Ireland
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Teacher Notes (Interactive)

Use this section to reveal answers during class discussion. This box will not appear if you print the page.

Reveal Q1 Solution

Answer: Friend 2
Logic: 9 + 5 = 14. 14 wraps around the 12-clock to become 2.

Reveal Q2 Solution

Answer: Friend 2
Logic: 50 divided by 12 is 4 with a remainder of 2.

Reveal Q3 Solution

Answer: No, Friend 6
Logic: (Start at 2) + 100 = 102.
102 modulo 12 = 6.

It's Computational Thinking

This puzzle explores Modulo Arithmetic (or "Clock Arithmetic"). In computer science, we often deal with cycles, such as seconds on a clock or animations in a game loop. Instead of counting to infinity, we count up to a limit (here, 12) and wrap around to the start. The formula used is (Current Position + Steps) modulo 12.

Computational Thinking Skills: Abstraction, Algorithmic Thinking, Pattern Recognition