After several years of on-and-off toying with IQ Blocks, I had finally figured out how many solutions there were (see here).
My new question was “How many pieces can be placed before it is not always possible to reach a successful outcome?” I assumed that for every way to place the first three or even four initial pieces that there would be a way to successfully place all the pieces on the board.
Believe it or not, I was very wrong. I should have noted that I had approximately 21,000 ways to put down three pieces, and about 224,000 ways to put down the first four pieces, and only about 101,000 solutions to the game (including scenarios which are identical under rotational symmetry). So obviously all four piece scenarios couldn’t lead to a solution.
I checked all possible three piece scenarios against all possible solutions, and found that most (12,310 out of 20,905) of the three piece scenarios can’t produce a solution. Even more interesting is that several of the three piece scenarios can produce over 300 solutions.
This scenario produces all of these solutions (365 to be exact).
This one produced all of these 356 solutions.
But all off these scenarios can’t produce any solutions.
Here is a challenge for all the skeptics out there; try to produce a solution from one of these.
Update; I noticed that this scenario can produce 621 solutions.
I was pretty surprised at the results.
I figured that every possible two piece scenario for sure could produce a solution. Again I was wrong.
Out of about 1,456 ways to place the first two pieces 1,329 produced solutions.
All of these two piece scenarios can’t produce a solution (another challenge for the non-believers).
I note that every possible one piece scenario can produce a solution. Phew!
The piece on the left can produce 3,312 solutions.
The second piece from the left can produce 4,753 solutions.
The next piece (light blue); 2,723 solutions.
Red; 4,810 solutions.
Pink; 6,615 solutions.
Light green; 4,074 solutions.
Orange; 5,351 solutions.
Blue; 4,886 solutions.
Yellow; 7,916 solutions.
Green; 6,456 solutions.
So it would seem that the best strategy would be to start by placing the yellow, dark green, or pink piece first, and to avoid putting the light blue or bright red piece first.
I found an article about strategy, and what I have found here seems to be consistent with his advice (for beginners).
(Also I noticed on his page that he provides the number of solutions as 12,724, which is the same as I provided in my last post on this topic. The author of that page told me that he corresponded with someone in 1999 on this topic, and that that person wrote a computer program to solve the game).