How it all started

In The Netherlands 67 is currently the retirement age. For me this happened in 2025 on

Jan	Feb	Mar	Apr	May	Jun	xxx
Jul	Aug	Sep	Oct	Nov	Dec	xxx
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31	xxx	xxx	xxx	xxx

My farewell party at the company was already a week before on

Jan	Feb	Mar	Apr	May	Jun	xxx
Jul	Aug	Sep	Oct	Nov	Dec	xxx
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31	xxx	xxx	xxx	xxx

You probably already guessed what I am showing: a photograph of the date on the physical puzzle, followed by a diagram which will be used elsewhere on this site.

One last photograph, the empty puzzle:

Back to the farewell party: my colleague Alex gave me A-Puzzle-A-Day, by the company DragonFjord.
At first glance I thought: "This is not for me, but I can automate this without much difficulty".

I was wrong twice: while trying to create a program I got interested in the puzzle and found some dates offline; not necessarily the current calendar date, but at least all pieces fitted somewhere leaving 2 squares open.

My first programming attempt turned out to be very slow. Naïvely I expected to calculate all possibilities using JavaScript within HTML. In short: just another page in my personal calculation Blogspot. As you are now reading this separate Blogspot, you understand this did not work out.

The JavaScript with HTML did not work, but the JavaScript code was still useful in the next attempt: standalone JavaScript creating HTML. This too turned out to be very slow.

But then I made a slight change: rather than creating 1 HTML file with all solutions, I created 366 HTML files, each with the solutions for 1 date. Also the 6 incorrect dates where handled: February 30 and 5 times the 31^st.

The results were astonishing: I expected less than a dozen solutions per date, but the average is almost 67, with a standard deviation of almost 38. You find the list in Statistics per category reverse sorted by number of solutions. As you can see from the standard deviation, there are enormous differences in the number of solutions per date, ranging from 7 solutions on October 6 to 216 solutions on January 25.

Now the question arises: can we predict/calculate the number of solutions per date? The answer is: hardly. At least not with the strategy chosen on this site: the number of filtered positions. What a filtered position is, will be handled in the Definitions section. For now it is enough to know that a position is the location of one of the 8 forms on the board, and a filtered location is a position that is not possible for a certain date.

For October 6 (with its minimum 7 solutions) a filtered position is any position where the form either covers the square marked Oct or the square marked 6. It turns out that for for October 280 positions are filtered out of a total of 961, 29%. The expectation is that the more filtered positions there are, the less solutions. Indeed January 25 (maximum 216) has only 134 filtered positions.

However, if you look at the minimum and maximum number of filtered positions, you notice there may be a trend, but a rather weak one: 

• January 29 has a minimum of 58 filtered positions, but only 74 solutions, only slightly more than the average 67
• September 11 has maximum of 366 filtered positions and 36 solutions, roughly the average minus the standard deviation

So there is some relation between numbers of solutions and filtered positions, but not a very strong relationship; the correlation factor of -0.28 hints in that direction. (0 means no correlation, -1 is a linear function y=Ax+B with negative A.)

We have taken 2 further attempts to investigate this further. The first attempt for to add extra pairs; not only dates, but also 66 double months and 465 double numbers. This gave a total of 903 pairs. Average and standard deviation were in the same range as before, so no surprises there.

BUT there was one really big surprise: 7 pairs without solutions. Hooray for DragonFjord, who managed to create a game with solutions for all dates. We now know, this is not to be taken for granted.

The second line of investigation was summarising per square. You find the results in Square summary reverse sorted by number of solutions. The correlation factor is now -0.42, which is an improvement, but not a breakthrough.

The summary of the story: All solutions are calculated, but it stays a mystery why the various dates have such differences in numbers of solutions.

The even shorter summary: I had a good time creating this site and I hope you will have the same when reading site, preferably in the order suggested in the above Table of Contents.

PS: another thank you for Alex, who was so kind to ask DragonFjord about license issues of the photographs. There seems to be none.