Easy to Expert: What Changes at Each Puzzle Level

Every game in Puzzle Picnic has four levels: Easy, Medium, Hard and Expert. Moving up a level makes the grid bigger, and, more importantly, the puzzle needs harder solving techniques. Sudoku goes from 6x6 grids solved with singles to classic 9x9 grids. Ships brings a bigger fleet, Expert Stars needs reasoning about groups of regions, Trail adds walls and Lines draws a bigger shape. A good time to move up is when your current level feels steady.

This post is for anyone choosing a level: beginners wondering whether to leave Easy, and regular players deciding whether Expert is for them. It explains how a level is decided, what changes in each of the six games, and how to tell when you are ready.

How a puzzle's level is decided

In Puzzle Picnic, a puzzle's level depends on which solving techniques it needs, not only on how big it is. Every puzzle is made by the app from a seed, so the same game, seed and difficulty always give the same puzzle. A solver then checks that the puzzle has exactly one solution and works out which techniques it takes to get there.

Grading by technique matches what research has found about how people experience difficulty. In a study of sudoku using data from hundreds of solvers on more than 1,700 puzzles, Radek Pelánek found that the number of given digits correlated only weakly with how long people took to solve (correlations of 0.25 and 0.27 in two data sets). A model of how humans actually solve, step by step, did far better, and combined with other measures it reached up to 0.95. Pelánek describes two sources of difficulty: how complex each single step is, and how the steps depend on each other (Pelánek, Difficulty Rating of Sudoku Puzzles, 2014).

So "fewer clues" is not the same as "harder". What makes a puzzle harder is a step you have not met before, or a long chain of steps where each one waits on the last.

Two things never change between levels. Every puzzle has exactly one solution, and logic gets you there: you never have to guess, on Easy or on Expert. The post on what "logic-only" really means explains why that matters.

The four levels at a glance

The table shows the grid at each level in every game. The sections below explain what else changes. The daily puzzle, one a day for everyone that rotates through the six games, is always Medium.

What changes in each game

Each game grows in its own way. In some the step up is mostly size; in others a new kind of reasoning appears at Hard.

Sudoku: from 6x6 singles to 9x9 techniques

Sudoku changes more between levels than any other game. Easy and Medium are 6x6 grids (digits 1 to 6, boxes of 2 by 3) that you can solve with singles alone: a square where only one digit fits, or a digit that fits in only one square of a row, column or box. Medium simply gives you fewer clues, 11 to 13 instead of 17 to 19, so you work longer before the grid fills in.

Hard and Expert are classic 9x9 grids, Hard with 27 to 31 clues and Expert with 23 to 27. These need harder techniques. The app's solver knows naked and hidden singles, pointing and claiming, naked and hidden pairs and triples, X-Wing, Swordfish, XY-Wing, XYZ-Wing, simple colouring and forcing chains. The sudoku strategies guide takes them in the order solvers usually meet them.

Bridges: more room, more islands to join

In Bridges, the grid grows from 7x7 on Easy to 9x9 on Medium, 9 by 12 on Hard and 11 by 14 on Expert. That is 49 squares on Easy and 154 on Expert, about three times the space. A bigger grid has room for more islands and longer bridges, and the rule that every island must end up connected in one group matters more, because there are more ways to cut off a small cluster by accident. The Hashi strategy guide covers the deductions that carry you through the bigger grids.

Ships: a bigger fleet and fewer squares revealed

In Ships, each level brings a bigger grid and a bigger fleet, and Easy reveals a few squares to start while Expert usually reveals none.

Expert is the classic fleet of ten ships. Notice the last column: the grid grows faster than the fleet, so a larger share of every Expert grid is water. That means more squares to rule out before the ships appear, and usually no revealed squares to lean on. The Battleship solitaire strategy guide shows how fleet accounting handles it.

Stars: one more row each level, and region groups at the top

In Stars, the grid grows by one row and one column each level, from 6x6 on Easy to 9x9 on Expert. Since every row, column and region holds one star, that also means one more star to place: six on Easy, nine on Expert.

The real change comes higher up. Expert puzzles need reasoning about groups of regions, and some Hard puzzles do too. The idea: if some regions fit entirely inside the same number of rows (say, two regions that lie wholly within rows 3 and 4), then those two rows' two stars must both go in those regions. Every other square in rows 3 and 4 is empty. The same works for columns. On Easy and Medium you can usually get by looking at one region at a time; on Expert, and sometimes on Hard, you start looking at several together. The Star Battle strategy guide has worked examples.

Trail: walls arrive, numbers thin out

In Trail, Easy is a 5x5 grid and Medium a 6x6. Hard is a 7x7 grid with thick walls, which the line cannot pass through, and Expert is an 8x8 grid with more walls. On both walled levels the numbers are trimmed to the fewest that still give one solution, where Easy and Medium always show at least eight. Walls also carry information: a wall next to a square takes away one of its exits, which can force the line's next move. Fewer numbers means fewer fixed points to steer between, so you rely more on corners, dead ends and the shape of the grid. The path puzzle strategy guide explains those techniques.

Lines: a bigger shape and longer tangles

In Lines, the shape gets bigger at each level: 11 squares across on Easy, 15 on Medium, 19 on Hard and 23 on Expert. The lines also get longer and more tangled. On the higher levels, the app places more lines in the path of other lines, so fewer lines are free at the start and the chains of lines that have to leave one after another get longer. The rule never changes, so Expert is mostly a longer, more careful search for the next free line. The Lines strategy guide covers how to find it.

The biggest jumps between levels

Some steps up are gentle and some are steep. Knowing which is which helps you set your expectations.

• Sudoku, Medium to Hard. The steepest step in the app. The grid goes from 36 squares to 81, the digits from six to nine, and singles stop being enough. Expect your first Hard puzzles to take much longer than Medium, and expect to start using notes.
• Stars, Hard to Expert. The grid grows by only one row, but Expert puzzles are chosen to need reasoning about groups of regions, which only some Hard puzzles need. If a puzzle suddenly feels stuck, this is usually the missing idea.
• Trail, Medium to Hard. Walls arrive. They help more than they hinder once you read them as information.
• Ships, Easy to Medium. The fleet grows from six ships to eight and a ship of length 4 appears, on a grid nearly twice the size.
• Bridges and Lines. These grow more evenly, mostly in size, so each step feels like more of the same rather than something new.

How to tell when you are ready to move up

You are ready for the next level when your current one feels steady: you finish most puzzles without a hint and without mistakes, and you rarely hit a point where you have no idea what to try next. Psychologists who study absorption describe something similar. In the account of flow by Nakamura and Csikszentmihalyi, one condition for becoming absorbed in an activity is a good balance between the perceived challenge and your perceived skills (Wikipedia: Flow)). Too easy feels dull; too hard feels anxious.

Some practical signs, as a rule of thumb rather than a formula:

• Clean solves in a row. In Puzzle Picnic, a solve with no hints, no power-ups and no mistakes counts as clean. Two or three clean solves in a row at one level is a good sign.
• Your time settles. The app records your time but nothing runs out. When your times stop falling at a level, you have probably learned what it has to teach.
• You can explain your moves. If you could tell a friend why each step was forced, you are using technique, not luck.

Then try one puzzle at the next level, with no pressure to finish it quickly. If it feels like a good stretch, stay. If it feels like a wall, go back for a while and come again later. A hint, which explains the next logical step, is a good way to learn a technique you have not met yet. A solve that uses one is marked as assisted, but it still teaches you something.

Moving back down is part of it

Easy and Medium suit experienced players too. A short, calm puzzle at a lower level is a good way to keep a daily habit going on a busy day, and nothing in Puzzle Picnic punishes it. Harder levels do earn more: solving fills a points meter towards a sticker pack, with more points for harder levels, for a clean solve and for the daily puzzle. But the meter fills at every level, and no timer presses you on any of them.

Many players settle on different levels for different games: Expert in the game they love, Medium in one they are still learning. That is a fine way to play.

Frequently asked questions

Is Expert just a bigger version of Hard?

Partly. In every game Expert has a bigger grid or shape than Hard. In some games it also takes something away: fewer clues in Sudoku, usually no revealed squares in Ships, and more walls in Trail. Less to start from usually means longer chains of reasoning.

Why are Easy and Medium sudoku 6x6?

A 6x6 grid uses the same rules as the classic 9x9 with fewer squares to track, so you can learn scanning and singles without feeling overwhelmed. Hard and Expert then move to the full 9x9 grid. The 6x6 sudoku guide explains the small grid.

Will a Hard or Expert puzzle ever need a guess?

No. Every puzzle at every level has exactly one solution, and the app's solver checks that it can be reached by logic. Harder levels need harder techniques, but there is always a next step you can prove.

Is the number of clues a good guide to difficulty?

Only a rough one. In Pelánek's study of sudoku solvers, the number of given digits correlated only weakly with solving time. The techniques a puzzle needs, and how its steps depend on each other, matter much more.

Where to go next

Pick one game and play a puzzle at the level above the one you usually choose. If it is Sudoku and you are on Medium, give yourself time, because Hard is the biggest step in the app. For how the levels are made and checked, read how a puzzle is made from a seed. You can play all six games in the browser at Puzzle Picnic, no account needed.

Sources

• Pelánek, R.: Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation (arXiv, 2014)
• Wikipedia: Flow (psychology))