School of Logic: a Collection of Puzzles involving the Student Six

by Coyotek4


Puzzle 20: Double Vision, Part 2

After several minutes of prepping in a separate room, Ocellus asks Smolder one last time: “You know what you have to say?”

“I got it,” the young dragon insists.

Satisfied, Ocellus returns to the dining nook and explains the next challenge to the others, with Smolder following close behind. “OK,” she begins, “for these five rounds, you’ll each see two Smolders, one of which will be me. Each of us will have a card from 1 to 4, and of course, we won’t have the same card. You’ll have to figure out which of us is really Smolder, as well as which card each of us has.”

The foursome look at each other quizzically, before Silverstream addresses the changeling: “Uh … how is this any different from what we just did?”

“One small change, but it makes a big difference: this time, if I have the 1 or 3 then my statements will be false, and if I have the 2 or 4 then my statements will be true.”

Ocellus’s comment is met be more strange looks. “That exactly how first five rounds went,” Yona points out.

Oh … yeah, that part’s the same.” Ocellus begins to blush as she continues: “What’s different is—”

“What’s different,” Smolder interrupts, “is that if I have the 1 or 3 then my statements will be true, and if I have the 2 or 4 then my statements will be false. It’s the opposite of Ocellus.”

“That … really doesn’t sound all that much more challenging,” Gallus states.

“Hey, I’m game either way,” Sandbar replies. “Go ahead and start.”

The foursome collectively close their eyes, and the rounds begin:

[In each round, one Smolder appears on the group’s left (L) and one appears on their right (R).]

[Round 1]
L: “I am Smolder. I have the 1.”
R: “I am Smolder. I have the 2.”

[Round 2]
L: “I am Smolder. Ocellus has the 3.”
R: “I am Ocellus. Smolder does not have the 4.”

[Round 3]
L: “I have the 1. The other card is not the 2.”
R: “I have the 3.”

[Round 4]
L: “The sum of our numbers is 5. My number is the smaller of the two.”
R: “One of our numbers is double the other. My friend’s card is not the 1.”

[Round 5]
L: “Either I am Smolder or I have the 3.”
R: “I am Smolder and I do not have the 4. Neither of us has the 2.”