I am an avid video game player, and the "Final Fantasy" series is one of my all-time favorites.
Fun Logic Puzzles From Final Fantasy
Welcome, time travellers! Are you stumped trying to solve Final Fantasy XIII-2's temporal rift clock puzzles? Are you tired of jumping around the "Hands of Time" hoping you'll land on the right numbers?
Here are some tips to help you solve FFXIII-2's clock puzzles without resolving to video game cheats to get through the game. Kupo!
The Basics: How the Clock Puzzles Work - Let's Review
Here's an example Temporal Rift clock puzzle. The rules are simple:
- The puzzle looks like a clock with 8-13 numbers. Each spot may be a digit from 1 to 6.
- Step on each number exactly once. Numbers disappear after you step on them.
- After choosing a starting point, you can only step on numbers the hands point to.
- Both two clock hands move the number of spaces indicated by the space you've stepped on. One hand moves counterclockwise, the other clockwise.
- If both hands point to blank spaces (where you've already stepped on and erased both numbers), you have to retry.
(This is Step 3)
How I Solve a Clock Puzzle
Like Suduko, it's a process of elimination.
- I walk onto the clock so I can see all the numbers, and then I sketch it.
(You could draw it on a sheet of paper, but I'm a nerd and use a graphics program, in this case Procreate for iPad/iPhone. Graphics programs let you draw the clock on one layer and notes on another, which you can undo/erase without touching the clock. Also, you can use color, making it easier to follow.)
- Note: on some clock puzzles, a timer starts when you step onto the board. Grrr. In that case, draw the TOP number on the clock face on your diagram, then hit square to retry and draw the rest of the clock without stepping aboard. If you scootch right up to the edge of the clock face, you can usually detect the top, off-screen number by noting the color glow up there: red = 1, orange = 2, green = 3, light blue = 4, purple = 5, pink = 6.
- Once you've drawn your clock, on a separate layer (if you're using a graphics program), draw arrows FROM each number TO each number it points to. For example, draw arrows from a 3 to whatever is 3 spaces away from it to the left and to the right.
- Now for the logic puzzle. You've just created a diagram of all possible moves. Your next job is to look for places where there's only ONE possible move to or from a particular spot on the board.
Once you've identified a single-option pathway, you note it by drawing it in black. Each time you identify a single-option pathway, it should eliminate possibilities and reveal new single-options by process of elimination.
How do we identify "one possible option" pathways? By using logic.
RULE: Every Spot Has Two Possible Paths AWAY From It
Rules of Logic for the Temporal Rift Clocks
RULE: you can (and must) land on each space only once.
Because of how the clock works, there's a few logic rules that can help us narrow down possibilities.
- All numbers EXCEPT the starting point and end point must have at least one path leading TO that spot, and one leading away from it. So if you discover a place with no paths leading TO it, it MUST be the starting point. Mark it accordingly: "S"!
- If a spot has only one path leading TO or FROM it, mark that path as a black arrow and try treating it as a single-option pathway. It may be wrong—it's possible the number is a start or end point—but usually, that means, "Here's the only way you can go from this spot, so you MUST go that way."
- Each number on the clock can only be the destination of ONE other number. So, whenever you arrive on a number, that rules out any OTHER pathways pointing to it. Follow those pathways back to their point of origin, and pick the OTHER pathway from that origin point, instead.
- For example, in the diagram above, once I've arrived at 4 via some other route, then I know that the 2 can't point to it and must instead lead to its alternate destination, 3. Therefore, after I reach the 4, I draw a black arrow from the two to the three.
- Once you've eliminated some "outbound pathways," you may find that one of the clock positions only points to spots you've already landed on. If you discover a place with no available paths leading FROM it, it MUST be the ending point. Mark it with an "E"!
- You must land on all numbers. So if you accidentally set up a closed loop before you've touched all the numbers, look for alternatives that will break the loop.
Let's walk through the example above.
Solving a Temporal Rift Puzzle: Example
Let's do this, kupo!
So here's that puzzle again. It looks as bewildering as a tangled kite string, but close examination turns up a few promising leads.
For example, on a board this size, the 5 MUST point to the spot on the exact opposite side of the board, 5 spots clockwise or counterclockwise. That means only one possible pathway leads out from the 5.
All Possible Paths Mapped
There's no spot on the board which has NO pathways pointing to it or from it. (Drat). So the start point and end point aren't easily identifiable.
However, there's quite a few places where there's only ONE pathway leading to or from a spot. We'll mark those in black, provisionally, keeping in mind that one of those could be a starting or ending point that requires no path leading to or from it.
Mark Single Inbound Paths
(I notice that I actually missed a one-inbound-path location in the diagram above. Look for a number that only has ONE pathway pointing to it. Can you see it? The 4 at the bottom of the clock can only be reached from the 1 to its right!)
Now we've gotten somewhere. Backtrack along each black line to the number pointing to it. If the black path is correct,* than the OTHER outbound path from its "origin point" is eliminated! So eliminate...scribble through, or just eyeball it... the "origin point"'s other pathway.
For example, once we know that the two at upper left MUST lead to the three at lower left, then the two's pathway to the 1 at upper right is eliminated as a possibility. But the only other way to get to that one is from the 4 at the bottom and...hey, we just eliminated that pathway, too! That means the one MUST be a starting point, because we've eliminated all the paths leading to it.
Just because there's only one possible path pointing to a location doesn't guarantee you'll take that pathway. It could be pointed at what turns out to be the starting point. So, just assume the "single inbound" paths are correct unless you run into a dead-end.
So here's what we know so far.
Backtracking, Eliminating Possibilities
We've settled quite a few pathways. Now I run into trouble: there's no "single option pathways" left... I can't find any more spaces with only one pathway leading to or from them. So now I have to make a guess and see if it works out. I'll use yet another color, brown, in case I have to back up, and yet another layer, so I can delete and try again.
It's time to make a choice.
I look for someplace that only has two remaining possibilities, and pick one. If it doesn't work out, I'll back up to this point and try the other possibility. So, arbitrarily, I pick the 3 on the right-hand side, which has only two pathways leading from it (of course), and pick one:
Trying Out A Possible Path (Brown)
This is good. If the three points to that two, then no other number can point to the two. So the two 4s pointing to that 2 must point to their alternate destination (if my guess on the last move was right). Therefore, using the "guess" color, I draw lines from those fours to their alternate destinations.
Backtracking Based On Last Guess (Brown)
Again, this is looking promising. Now that we've chosen the bottom righthand 1 as a destination, no other number can point to it. That means the two at lower left must be the ending (both its destinations have been eliminated) or else the choice of the 3 I made a moment ago was wrong.
It also means that the three at left can't point to the 1 just eliminated, so it must point to its alternate destination, the 4 at the top. I notice that I have now got pathways pointing to or from all the numbers. Time to take stock. Does this form a continuous path with just one start and finish?
Does It Work?
Oops! No! Starting at the 1, we wind up at the 2 marked E? but haven't touched all the numbers. All the remaining numbers are trapped on their own closed, separate loop. Let's back up to where I made that choice and think carefully.
The last time, I made an arbitrary choice drawing a path from the 3 at the right to the 2 on the bottom. I then assumed that both 4s pointing to that 2 must point to their alternate destinations, since they can't point to the 2. But that's not so if one of the 4s is a stopping point. So forget the 4s. Let's go about this differently and say, "If the 3 points to the 2, where does the 2 point next?"
Try the Other Option
It's gotta be the 1! Otherwise, if it points to the 5, we've got a closed loop: 3-2-5-3-2-5...etc, etc.
At that point, I see that I've eliminated both possible destinations for the 4 at the top of the clock (because it can't point to spots that have already been "claimed" by a previous step). So that 4 at the top must be the endpoint. Furthermore, the 4 on the right must point to the 5, because its alternate destination, the 2, has been claimed as a destination of the 3.
Testing the Alternate Route
AHA! I think we've got it. There's only one orphaned number left—the 4 at the top is looking lonely—and when we hook up the only remaining number that could point to it, the three at lower left... we've got a solution that works! It touches every number exactly once.
This puzzle was actually the hardest one I solved. They're usually easier than this, and often, you're never forced to make an arbitrary choice.
Recap: How to Solve the Clock Puzzle
- Draw the puzzle.
- Sketch ALL the possible pathways connecting one number to the next. (That is, mark each of the two possible destinations for each number.) These are the colored lines on my chart.
- Look for numbers which have no pathways leading to or from them. These are starting or endpoints.
- Look for numbers which have only one pathway leading to them. These are (we hope) not starting or endpoints, but one-option-pathways. Mark them in black.
Once you've identified all the one-option pathways, look for a spot where one of two possibilities is probably true. In a different color (if possible), pick one of those pathways and explore it.
- Avoid causing closed loops.
- Once you've arrived at a number (a destination), all the other pathways pointing to it...can't! So backtrack along those pathways to their "origins", and point those "origin" numbers to their alternate destinations.
- In the end, no more than one path can point to or from each number.
- If you get stuck, that probably means you just tripped over a starting or ending point.
© 2012 auronlu
Youatmines on December 04, 2015:
I created an account just to tell you thank you for writing this! It was really fun to figure it out, without actually cheating! Thank you!