A-puzzle-a-day solutions for January

16th January 2021

As an early family Christmas present, I backed A-Puzzle-A-Day on Kickstarter, a puzzle calendar which you can now purchase directly from Dragon Fjord. Every day is possible, sometimes more than once, and some days certainly seem easier than others!

Some solutions give you multiple days in one, by a flipping or rotation of a piece or two, or a small rearrangement. Below (spoilers!) I include the solutions I have found for January, with markings showing how they work together. A red dot means this is the only solution I have found containing that solution, and a green dot means this pattern solves that day but so does another pattern listed.

1^st (and also 2^nd, 3^rd, 13^th, 14^th, 20^th, 21^st, 27^th, 28^th)

This arrangement for 1st January also gives us not only five other dates, through rotating the b shape and swapping it with the rectangle, but another three by turning over the t shape and swapping the c and the b shapes, and then flipping/swapping the c shape and the rectangle.

4^th (and also 5^th, 6^th, 7^th, 11^th, 14^th, 18^th, 21^st, 25^th, 26^th, 27^th, 28^th)

Three pieces make up a 4x4 square lacking one space, which gives us the four corners; plus with a slight rearrangement swapping the two l-type pieces, a different holed-square giving us the other eight edge spaces.

8^th (and also 9^th, 23^rd, 30^th)

This solution gives us three other days with flipping and swapping the c-shape and the rectangle. I have found solutions to some days which only give that day and no other, but have ignored those here in preference to multi-day solutions.

10^th (and also 2^nd, 3^rd, 4^th, 9^th, 11^th, 22^nd, 23^rd, 24^th, 29^th, 30^th, 31^st)

Using a similar trick to 1^st, we cover twelve different days through flipping the t-shape and swapping the c/b-shapes and rectangle.

12^th (and also 13^th, 15^th, 16^th)

Another c-shape flip/ rectangle swap for 15^th, and some other days we have already found through other means.

19^th (and also 3^rd, 4^th, 9^th, 16^th, 19^th, 24^th, 25^th)

This solution I did not find myself, but saw Robin mention on Twitter; I think I was stuck on 9^th at the time (even though we had already found it via 8^th, we were not being very methodical!). It is another 4x4 square providing eight solutions by rotation and flipping, but no way to add the corners as with 4^th.

17^th (and also 10^th, 20^th, 21^st)

Lastly, to catch 17^th, another solution with a c-shape flip/ rectangle swap.

Alternate solution for 22^nd (and also 5^th, 6^th, 23^rd, 24^th, 29^th, 30^th, 31^st)

Robin’s sister found this solution that is another way of getting 22^nd and 29^th, along with a variety of others, utilising the t-shape flip solution again.

Conclusion

As we have seen above, all of January can be done using only three patterns:

• A simple four-day solution where you flip the c-shape and swap it with the rectangle;
• An expanded form of that where, with a flip of the t-shape the c- and b-shapes can be swapped, providing another round of solutions, up to twelve in total;
• A square shape with a hole made up of three shapes that can be rotated or flipped to provide eight or twelve solutions (perahps with an l-shape swap).

Every January result I found uses the chair shape either around or next to the January space. I assume a whole different set of techniques may be needed for February…