You hear someone in the next room roll two dice.

“Look at the two numbers. Do you see an odd number?”

“Yes”

Now, what is the probability that he rolled two consecutive numbers? For example, 3-2 or 5-6

Enter your solutions at Solutions: consecutive dice.

Clarifying Information

You can’t see the dice.

“Do you see an odd number” refers to the face of at least one die, not the sum.

Credit

This is nothing new. But a discussion at If-Then Knots put it in my mind. Then when the Carnival of Mathematics #46 at Walking Randomly linked to Tanya Khovanova’s blog, I visited, poked around, and found this related puzzle with explanation.

1. December 30, 2008 pm31 8:53 pm 8:53 pm

What is the probability that the person in the other room is lying?

Your puzzle tricked me the first time through, but that’s no surprise — I almost always fall for things like this. At least I have learned not to be satisfied with my first answer, especially if it seems like the “obvious” shortcut.

2. December 31, 2008 am31 12:26 am 12:26 am

A related problem appeared in the very first Carnival of Mathematics.