Calendar Puzzles

What is a calendar puzzle?

A polyomino calendar puzzle, sometimes called “A-Puzzle-A-Day” or similar, is a fun daily challenge where you’re tasked with arranging puzzle pieces on a square grid to reveal just the current day and month.

How does it work?

Let’s take a look at this example puzzle below, which only uses the days of the month with numbers 1 through 31, as shown on the left of the following figure. Each day is in its own square, so the board has a total of 31 squares within a rigid boundary.

example Puzzle #1

As shown in the right, this example uses six different pentominoes, each made up of five squares and with different color above. Since six pentominoes cover exactly 30 squares, when you try to fit them all onto a 31-square board, you’ll end up with one square left uncovered. Your challenge is to pick a day of the month—like today—and then rotate, flip, or shift the pieces until only your chosen day is left visible! As you can see, the arrangement of pentominoes on the right solves Day 17.

Why designing new ones?

There are lots of calendar puzzles available online, each with its own design and difficulty level. I’m excited to share some new designs with you, hoping you’ll enjoy them as much as I do!

• easier puzzles than those you might find on the market, perfect for beginners. 
• a great daily cognitive exercise for older adults and kids, helping them build problem-solving skills, improve short-term memory, focus, and develop spatial reasoning.
• puzzles with different levels of difficulty, so you can tackle more challenging levels as you get better at the puzzle
• free and downloadable designs in SVG format, so you can use them to 3D print or laser cut/engrave for yourself, family, and friends

What puzzles are you offering?

This is a list of upcoming calendar puzzles which will be offered here

• Boards with square grid
• Day of the month
• Month + day of the month
• Month + day of the month + day of the week
• Boards with triangle grid
• Day of the month
• Month + day of the month
• Month + day of the month + day of the week
• Boards with hexagonal grid

What does calendar puzzle design involve?

Designing polyomino calendar puzzles requires a few key considerations:

• designing a board: figuring out the layout of square units and how to arrange the dates. 
• choosing a symmetric board: this makes solving easier because you can rotate or flip a single solution to solve multiple days. Take Puzzle #1 above as an example; you could take the winning solution for Day 1, flip it horizontally, and instantly solve Day 7
• choosing an asymmetric board: usually makes finding a solution more challenging.
• square units: we need enough square units to cover all the dates. In a calendar puzzle with only days of the month, we need at least 31 square units. Usually, the square units are arranged in a continuous line, but there are some designs that do things differently later on.
• choosing a set of polyomino pieces: there are lots of polyomino pieces, and we need to pick the right set to
• cover the total square units on the board, minus the number of dates we’ve chosen to solve (that is, left visible). In Puzzle #1, we need to cover 30 square units, which is 31 (from the board) minus 1 (from the chosen date to solve)
• solve all the possible dates with at least one solutions. Computer simulation is super helpful here to help us with this task. Usually, having more polyomino pieces makes it easier to solve the puzzles.
• additional design constrains: For example, it might require using only one side of all the pieces. This is something we’ll talk about in later example Puzzle #2.
• selecting design candidate: Sometimes, when there are more than one feasible designs that meet the above considerations, we can think about a few extra things to help us pick the final choice: 
• difficulty level, based on how many solutions are possible.  The puzzles are easier (or harder) when there are more (or less) available solutions from computer simulations.
• board aesthetic, to achieve a specific theme and idea
• polyomino pieces
• use only unique pieces or intentionally introduce duplicate pieces
• use only the same type of polyomino (for example, pentomino only), or allow a mix of different types

Let's use another puzzle design for solving the Day of the Month to explore several design features discussed above.

example Puzzle #2

The key differences of this Puzzle #2 against Puzzle #1 are:

• Puzzle #2 board has 180° rotational symmetry (instead of the horizontal flip symmetry in Puzzle #1), which means you can rotate the solution from Day 1 to solve Day 31!
• Unlike Puzzle #1 which uses 6 pentominoes (each covering 5 squares), Puzzle #2 uses 4 pentominoes, 1 hexomino (covering 6 squares) and 1 tetromino (covering 4 squares). Some puzzle enthusiasts would prefer Puzzle #1 since it uses only one type of polyominoes.
• Puzzle #2 has an average of 35.7 solutions per day, making it a bit easier than Puzzle #1, which has an average of 20.1 solutions
• Puzzle #2 also has a challenging hard mode! When you rotate and shift the 6 polyominoes as shown in the picture above, but without flipping, you can still solve all 31 days, though it’s much tougher with only 2.56 average solutions per day. That is, Puzzle #2 offers two ways to play
• easy level: all pieces are allowed to flip, rotate and shift 
• one-sided hard level: all pieces are allowed to rotate and shift, but not flip. To achieve this, the physical puzzle pieces will need to be marked on the proper sides.
• As a matter of fact, the one-sided requirement was considered during the design search. However,  6 pentominoes is not able to achieve this requirements.  That is, not all 31 days are solvable within all possible combinations of 6 different pentominoes and all permutation of their flips.