Levels that can be solved in fewer than the official number of moves

SPOILER ALERT. This post contains solutions to levels 3-23, 3-25, 4-8, 5-5, 5-6, 5-15, 6-1, 6-8, 6-9, 6-10, 6-11, 6-13, 6-18, 6-19 and 6-21.

Note: for notation used in this post, see my notation page here.

Second note: This post is about Version 2.2 of graBLOX: here are two ways to find out which version of the game you have.

Finally, to the post! More recent versions of graBLOX have, at the top of each level, some sort of “recommended number of moves” which one is supposed to solve the level in. For 15 of the levels (in Version 2.2 of graBLOX), one can actually do better! Here are the levels, each with a solution in fewer moves than the recommended number. The solver in each case is given in brackets after the solution.


 * ) 3-23: 6-move solution is 1.h1 2.g10 3.g9 4.a1 5.d7 6.b1. (my son)


 * ) 3-25: 6-move solution is 1.a12 2.g11 3.b5 4.g5 5.f2 6.c8. [in fact there are 7824 ways to solve this level in 6 moves!] (computer)


 * ) 4-8: 1.d9 2.e6 (me)


 * ) 5-5: 1.f8 2.c8 3.h1 4.h8 5.b11 (computer)


 * ) 5-6: 1.b11 2.e11 3.f7 4.c3 5.d7 (computer)


 * ) 5-15: 1.d4 2.e10 3. a5 4.g1 (me)


 * ) 6-1: 1.b11 2.g9 3.c3 4.h5 (computer)


 * ) 6-8: 1.f3 2.d5 3.h7 4.f11 5.c10 6.a8 7.a2 (me) (my computer ran out of memory looking for a 7-move solution so I had to find one by hand )


 * ) 6-9: 1.h8 2.d10 3.a3 4.e5 5.b12 6.g1 (computer)


 * ) 6-10: 1.a5 2.h8 3.f2 4.b10 5.g1 (computer) (I still think it’s very cool that this one is possible in 5 moves)


 * ) 6-11: 1.a7 2.e6 3.e10 4.d12 5.d4 6.a3 (computer)


 * ) 6-13: 1.c9 2.f6 3.c3 (computer)


 * ) 6-18: 24-move solution is (deep breath) 1.h9 2.h12 3.h7 4.b6 5.c10 6.h7 7.b6 8.h7 9.h9 10.h12 11.f9 12.e12 13.a11 (destroying 3 blocks) 14.h12 15.c10 16.f9 17.e12 (destroying 3 blocks) 18.h9 19.b6 20.c10 21.f9 (destroying 3 blocks) 22.h7 (activating Dizzy and destroying 3 more) 23.c2 24.c1 (me)


 * ) 6-19: 1.h2 2.d9 3.d5 4.h12 5.e5 6.b6 7.c1 (me)


 * ) 6-21: 1.h7 2.a1 3.d8 4.h11 5.c9 (computer)

Notes: Thirteen of the 15 solutions here are known (by brute force computer check) to be solutions in the minimal number of moves. The two levels I’m not sure about are 6-8 (is there a solution in 6 or fewer moves?) and 6-18 (is there a solution in 23 or fewer moves?) Both seem unlikely but I haven’t rigorously ruled these possibilities out.

What of the other 150-15=135 levels? For these, the recommended number of moves given in graBLOX v2.2 is indeed the minimum number required to solve the level (modulo bugs in my computer code etc).

The assertions above of the form “this is the minimum number of moves needed to solve the level” were typically verified using a computer program I wrote, so the truth of those assertions depends on the correctness of the code. One issue with my code is that I do not actually understand all of the game logic :-/ I am more explicit about these issues over here.