Image © E-GEMS. Used with permission.

Puzzle: The Hexagon Puzzle

In the story, Julie has to cross a chasm, spanned by a bridge "made of polished granite hexagons. On the surface of each hexagon was a number carved exactly in the middle." There is a path through the hexagons that follows a mathematical rule (e.g. all primes, all perfect squares, all multiples of 6). The task is to get Julie across without making too many wrong guesses; for each wrong guess, a dragon appears breathing fire and creates a pit that obliterates the number on that hexagon. After a certain number (which is dependent on the level) of encounters with the dragon, Julie 'dies,' and the player must try again with a new pattern.

Dialogue

R is playing Phoenix Quest for the second time, while E and A are both first-timers.

--R: Now we gotta get her across, we gotta get her across, ok, this is the little person, ok, her name is Julie and you have to get her across to the other side. Ok?
--A: By doing what?
--R: Ok. There's a pattern, ok, she's on 10 so we know 10 is ok. Now like if, last time it was by 3's. Ok. So like 13, 16, you know and so on and so on. So there's a pattern so...
--A: Does it matter which, can it be any of these or does it have to be able to touch?
--R: It can be any one that it's touching. So one of these... (uses the mouse to show which adjacent hexagons it could be)
--E: Um... ... It's that, I think. (pointing)
--R: What, 18?
--E: (quietly) Well 8 and 8. And that's 8. And that's 8.
--R: Then what. Oh then that's 8.
--A: Yes! Good.

They try E's pattern and are quite successful. (going up by 8's: 10, 18, 26, 34, 42, 50, 58, etc.) They work together to get across, calling out numbers, seem unfazed when the path goes both forward and backward across the board before Julie gets to the other side.)

--A: We got across, yay!
--R: Ok which path did Julie follow? (A, to other group: We figured it out.) The next number is 8 greater than the previous one. Ok.
--A: We did it!
--R: Ok. You got it. ... You have won.

The three-way conversation here focuses primarily on the math - on making guesses about the pattern, remembering what other patterns looked like, and checking that their choices are correct by following through the sequence. All three girls are actively involved and care about succeeding. It is clear that they understood their pattern well enough to choose it from a list of possibilities after Julie finally reached the other side.

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