Zendoku tactics


An easy Zendoku board.

1. Introduction

This article describes some useful tactics for Quest Mode in Zendoku. I’ll assume that you already know how to solve sudoku puzzles, at least in pencil-and-paper form, but that you need some tips for beating the later rounds of the quest.

2. Basic tactics

Focus on accuracy first. The penalty for making a mistake is high and gets higher as the quest level goes up. So don’t mess up. It’s usually worth checking your deductions and only rarely worth guessing (but see “Guessing” below for when it might be appropriate to guess).

Second, work on your speed of deduction. That may mean changing your approach: what works well in pen-and-paper sudoku doesn’t necessarily work well here. See “Scanning” below for a fast technique.

Third, improve your minigame speed. Some of the games have a secret that allows you to complete them quickly. This is what the Attack Box is for.

3. Delaying

Sometimes it is wise to delay placing a symbol. There are several reasons why you might do this.

First, as the master says, “An attack made while your opponent defends is a wasted attack.” If your opponent is already under attack, it’s a good idea to hold back your next attack while you make progress elsewhere on the board. When your opponent is done, you can unleash your next attack. Listen to the audio and you can hear when the attack is over. (You may find it helps to turn the music off in order to hear this clearly.)

When you’re under attack, the same consideration applies in reverse. If your enemy makes another attack while you’re still defending, it’s often useful to hold off completing the current attack until just after the new attack has landed, thus causing it to be wasted.

Second, you want to maximize the number of attacks you make. You get one attack for each row, column, block and symbol you complete, so in theory there are 36 attacks available. However, sometimes you’ll complete two sets at once: for example, the symbol that completes a block also complete a row. This means you only get one attack instead of two. In the worst case, a single symbol can complete four sets -- if you did this every time you’d only get nine attacks!

Normally, there’s not much you can do about this, especially with all the other things you are trying to think about. But some simple cases are easy to spot. Consider this position:

If you play the sword at B and then the dragon at A, you get one attack.  But if you play them in the other order, you get two attacks.

Here it’s obvious that a dragon goes at A and a sword at B. If you play the sword first and then the dragon, you get one attack. But if you play them in the other order, you get two attacks.

Third, make good use of your lucky symbols. Don’t play them immediately you deduce them, but save them so you can reflect an attack. Don’t waste your time looking at the attack rail; listen to the audio and you’ll hear when the enemy launches an attack.

These three techniques all involve deducing symbols but leaving them unplayed. This makes subsequent deductions harder, so you have to be careful. Speed and accuracy are still paramount, so don’t leave more symbols unplaced than you can comfortably remember. I can generally leave any number of lucky symbols unplayed as long as they are the last symbol in their row, column, or block. But otherwise I can only cope with one or two unplayed lucky symbols at a time, or else I spend too long repeating deductions to recover information that I already know.

4. Scanning

This is the basic technique that all sudoku solvers are familiar with, and in Zendoku it’s the fastest technique for making deductions. Pick a symbol and imagine blocks, rows and columns emerging from each occurrence of the symbol. Then look to see where the board is covered most densely by these imaginary rectangles, and pick out the spots where that symbol must go.

Here’s an easy board with no symbols played yet.

Consider scanning for yin-yang symbols on this board.

Let’s consider the yin-yang symbols The yin-yang symbol. Imagine rectangles emerging from each yin-yang symbol to cover squares in which you can’t put a yin-yang:

Red rectangles emerging from each yin-yang symbol to cover squares in which you can’t put a yin-yang.

That immediately reveals the remaining four squares where the yin-yang must go!

However, it’s probably a bit hard to visualize all that at once. You can make it easier by considering one block at a time. By considering blocks you make things as easy as possible for yourself because you can ignore the four-ninths of the board that can’t impinge on the block you are considering at the moment. So let’s consider just the bottom centre block and the parts of the board that might impinge on that block:

The sections of the board that might impinge on the bottom centre block.

Imagine rectangles emerging from the yin-yang symbols and covering squares in the bottom centre block. That gives the square for the yin-yang:

Red rectangles emerging from each yin-yang symbol to cover squares in which you can’t put a yin-yang.

Then you can go on and consider the other blocks in turn. This technique has the useful property that you can often keep going, making new deductions without having to reorient yourself, since the imaginary rectangles are still valid. You can just add the rectangle from the new symbol to your imaginary diagram and see if you can make any more deductions. In the example under consideration, the yin-yang you just placed gives you another one in the central block:

After placing a yin-yang in the bottom centre block, it is now possible to place another yin-yang in the middle centre block.

A sequence of deductions like this can be carried out quickly because there is no need to switch symbols. (However, as the boards get harder the opportunities for making multiple deductions without switching symbols become much rarer.)

5. Contingencies

When scanning, you may find a block in which there are multiple positions for a symbol that all lie in the same row or column. Consider scanning for umbrellas in this position:

Consider scanning for umbrellas in this part of the board.

In the centre block there must be an umbrella on one of the squares marked A:

In the centre block there must be an umbrella at A.

But whichever square the umbrella lies on, it eliminates the same set of squares in the left-hand block. That leaves only one place for the umbrella:

With an umbrella at A, there’s only one place for an umbrella in the left-hand block.

You could also have made this deduction by considering the question “where could an umbrella go in the second row?” But how would you have discovered that particular question to ask? If you’re scanning anyway, it’s more efficient to make the deduction like this.

Here’s a more complicated situation with a similar deduction. Consider scanning for swords in this part of the board:

Consider scanning for swords in this part of the board.

In the top right block, you can deduce that there must be a sword in one of the two squares marked A:

In the top right block, there must be a sword at A.

Whichever square the sword is in, the same set of squares are eliminated in the top left block, leaving only a single position for the sword in that block:

With a sword at A, there’s only one place for a sword in the top left block.

6. Guessing

In Quest Mode, the penalty for making a mistake is severe. But not so severe that you might not consider making guesses deliberately.

Guesses often work out, because it can be better to take the penalty and make progress rather than remain stuck on a deduction and make no progress. The AI is programmed so that it doesn’t speed up towards the end of the game, except to the extent that the deductions get easier. But human players can speed up a lot as the board gets full and the available options are reduced. Often the last half-dozen squares can be filled in only a couple of seconds. This means that you need not feel too bad about being behind in health: you’ll be able to catch up later. And being behind is an advantage in that the attacks you have to deal with are weaker.

Make guesses wisely. Fifty-fifty guesses are easy to spot but at higher levels of play are only worth the risk if you’re really stuck. But very often you can guess with a better than fifty-fifty probability of success. For example, consider the possible positions for the dragons in this part of the board:

Consider the positions for dragons in this part of the board.

There are four possible arrangements for the remaining two dragons. In one arrangement there is a dragon at A, but in three arrangements there is a dragon in one of the three squares marked B.

In one arrangement there is a dragon at A, but in three arrangements there is a dragon at B.

In the three cases where the dragon appears in one of the squares marked B, the other dragon goes in the square marked C:

With a dragon at B, the other dragon must go at C.

So if you play the dragon at C right away, you have a three-in-four chance of being right. If you’re stuck (or if you think that the only available deductions will take a long time), this might well be the best available play.

7. Watching your enemy

Your enemy is solving the same sudoku puzzle that you are solving, except that the symbols have been permuted so that you and he have lucky symbols in the same positions. This means that information about your enemy’s board may be useful to you.

If you listen carefully to the sounds your enemy is making, you can hear him playing. The length of time he takes can be informative, since he’s programmed to play easy deductions more quickly than hard deductions. You can also hear a different sound when the enemy plays his lucky symbol. That can be a clue as to an easy deduction involving that symbol.

Look at your enemy’s combo meter to see what kind of set he’s managed to complete. A row, column, or block shows up in the combo meter, but completing a set of symbols does not.

The type of attack is also informative. A fight attack (with a mini-enemy in the middle throwing fists or other objects at you) results from the completion of a set of symbols (and no other sets). Other attacks result from completion of a row, column or block. If you get a hit attack (with small squares of paper, wood or stone) then the location of these squares tells you which row, column, and block your enemy has just completed.

Near the start of a round these may provide useful information about where to make deductions.