Calendar Puzzle, Month + Day of the Month, Square Grid, Multi-level Challenges

 

Introduction

As one of the calendar puzzles, this puzzle takes the Day of the Month puzzle to the next level by adding months. Now the board has 12 extra squares representing January to December, as you can see in the image below.  This makes it a bit like the classic A-Puzzle-A-Day. However, our puzzle has a unique board layout and some multi-level challenges that we’ll explore later.  Just like the Day of the Month puzzle, this one uses the same six polyomino pieces, plus two new ones, bringing the total to eight polyomino pieces, as shown in the image below.

Just a heads-up: each of the eight polyomino pieces has a dot on one side, as shown above. The other sides are clear

You can find the svg file for laser cutting/engraving machine at Cutting Paths

How to Play?

Think of it as a fun twist on A-Puzzle-A-Day! Your goal is to cover all the squares with the eight polyomino pieces, except for the target month and day. Here are three ways to play:

1. Easiest: Give it a shot by rotating, moving, and flipping all eight pieces, but don’t worry about the dots. Computer simulations show that there are about 533.8 solutions per date from all 366 dates, and every date has at least 84 solutions!
2. All dots: Turn and flip all the pieces so the sides with Dots are facing up, then try to rotate and move these eight pieces, without flipping, to solve the puzzle. With this "all dots" rule, cthere is an average of 26.2 solutions per date from all 366 dates, every date has a minimum of 4 solutions.
3. No dot: Turn and flip all the pieces so the sides with No dot are facing up, then try to rotate and move these eight pieces, without flipping, to solve the puzzle. With this "no dots" rule,  there is an average of 20.7 solutions per date from all 366 dates, every date has a minimum of 2 solutions.

If you’re new to calendar puzzles or these eight polyomino pieces, it’s a good idea to start with the #1 easiest mode. Once you’re comfortable solving the puzzle without too much trouble, you can try the All dots or No dot challenges. Here’s a table that shows the total number of solutions available per date for these two challenges. Do you find it harder to solve the dates with orange highlights, which have fewer solutions than the others? If you didn’t quite nail every single piece of the challenges, think of it as a fantastic step forward and a fantastic reason to keep pushing yourself!

Total number of solutions per date for All dots and No dot challenges

Even the Dot Challenges Are Easy for Me, What's Next?

Can you find ways to come up with more solutions from what we already have?

The eight polyomino pieces in this puzzle are pretty flexible. They can stick together to make small areas that look like rectangles or squares, like you can see below. If your solution has these kinds of small areas, you can turn them around to make even more solutions! It’s often the case that when there are lots of solutions to choose from, some of them might have these types of small areas.

The small areas can take on different shapes, but they can still rotate. Here’s an example to illustrate:

You can also flip some small areas (with mirror symmetry), but that won’t help with the dot challenges anymore.

Sometimes, you might get a chance to swap two small areas if they have the same shape, like this:

Is it straightforward to create tomorrow’s solution using today’s?

Some of the pieces have symmetry, which lets them rotate and create solutions for different dates. For instance, if you rotate the ‘U’ piece below, you can transform a Day 9 solution into a Day 10 solution

And guess what? If you’ve got the following setup for Day 9, you can whip up solutions for Days 10, 11, and 12 in no time!

Could you please avoid using the ‘U’ piece to enclose squares for Month or Day of the Month?

It’s quite common to see the ‘U’ piece used to hold the target Month square or Day of the Month square, especially since it has a single square hole in the ‘U’ piece below.

If you fill the hole of 'U' piece with other pieces, are there still solutions? Well, yes, for most dates, but there are 48 dates out of the 366 where it’s not possible, as you can see in the table below

Total number of solutions per date for All dots and No dot challenges by filling the 'U' piece hole

So, for those dates with available solutions, can you find one?

Other polyomino pieces

There are other sets of polyomino pieces for the same board as shown here that could make the puzzle even more challenging. I’d be happy to share them if you’re interested!

Next Puzzle? 

See this one with additional day of the week