# Ring-theoretic riddle

You are given a ring for which 1+1=3 and 9/12=0. Yet this ring is not trivial, quite the opposite. What is your answer?

• @GentlePurpleRain I would think that any ring (in some sense of the word?) that fits with the puzzle would work. (Of course, in the typical sense, there is no such thing, since $1+1=3$ and $9=12\cdot 0$ describes the trivial ring only) Commented Feb 1, 2016 at 22:21
• @MiloBrandt I guess I didn't phrase my comment clearly. I was trying to point out that the OP doesn't actually ask a question. It says, "You are given a ring..." and then asks, "What is your answer?". It should either say something like, "Come up with a ring for which..." or it should ask something like, "What is the ring you were given?". Commented Feb 1, 2016 at 22:25
• @MiloBrandt actually $9=12 \cdot 0$ works in any ring of characteristic 3. Whereas $\frac{9}{12} = 0$ does trivialize the ring in the typical sense because it requires 12 to be invertible. Commented Feb 1, 2016 at 22:36
• The amount of downvotes on this question is appalling.
– dmg
Commented Feb 5, 2016 at 14:00
• @GentlePurpleRain Have a look at the answers, and you will see that the question is phrased perfectly.
– dmg
Commented Feb 5, 2016 at 14:02

No, I'll not marry a stranger from the internet

The ring is

An engagement ring (see hexomino's reasoning) - definitely not trivial!

• Yes, that makes more sense. Commented Feb 1, 2016 at 23:52

The Circle of Life.

because

1+1=3 refers to a man and a woman coming together to make a man, woman and child. 9/12 refers to 'nine months' at which point a baby is 0.