My puzzles

Solution: The Ladder / The Crystal

This is the solution for The Crystal puzzle / The Ladder puzzle.

There are many sizes for this puzzle, the solution shown here will use the two sizes I own (size 7 on right column and size 15 on left). The given explanations are generic enough to apply to any size you could face.

The different pieces will be identified using a letter and a number:
The 3 central axis will be assigned the letter C. The piece with a specific cut out will be C1 and the two other identical ones will be C2.
The pieces which can be described as full blocks with only a single cut out on half their depth in their middle will be assigned the letter F. Numbers will sort them by increasing length (F1=3, F2=5, etc). Comment: in this group is also placed the special 3 blocs long piece which has a 3/4th cut out in its middle instead of the usual half. this piece will be named FK to easily identify it.
The pieces close to the F blocks F but having an additional size-1 cut out on each side of their middle cut out will be labelled with the letter L. Numbers will be used in increasing order (L2=5, L3=7, etc).
Comment: there are no L1. As a matter of fact, if you reduce a L2 block to only 3-blocks size, the shape will in fact be the F1 one.
The pieces looking like the L blocks but with their cut outs going all the way to their extremity except for the very last block will be labelled with the letter H. Numbers are used in size increasing order (H3=7, H4=9, etc).
Comment: There are no H pieces in a crystal below size 11. The H pieces start with size H3 because if you reduce one to H2 (piece length=5) the cut outs will be only 1 block length and will in fact become identical to the L2 piece.
So, in identification, a F1 piece could as well be seen as a L1 and a H1. Moreover, a L2 piece can as well be seen as a H2. If you did not catch the idea, no big deal. It just helps understanding the group split shown below but is not required to follow the solution.

Let’s start by sorting the different pieces in groups (Crystal 15 above, Crystal 7 below):

Groupe C: contains the 3 main axis, the 3 C pieces.
Groupe F (x2): contains a decreasing series of F pieces from size F((N-3)/2) to F1 — where N is the crystal size (15 et 7 dans mes versions).
Groupe L (x2): contains a decreasing series of L pieces from L((N-3)/2) to L2 + one F1 (equals a L1) in one of the group and the special FK piece in the other (important).
Groupe H (x2): contains one F((N-3)/2) piece plus a decreasing series of the H pieces from H((N-5)/2) to H3 then a L2 piece (equals a H2) and a F1 piece (equals a H1).
Groupe G (x2): each contains deux series (stacked on the picture above) of decreasing F pieces from F((N-5)/2) to F1.
Groupe X (x2): contains the remaining F pices. Which are (in each X group) 2 F1, then 2 F2 with 2 F1, then 2 F3 with F2 and F1, etc until F((N-7)/2). Comment: The crystal 7 does not have any X group. ((7-7)/2 = 0 -> no possible piece there)

Sort your pieces as shown above and get used to my naming conventions so you’ll have a smoother experience in the following solution:

  1. Assembling the L and G groups:

    Crystal15-S2 Crystal7-S2

    Assemble (two times) one L group with one G group by inserting in the cut outs of each L piece the two F pieces whose length is just 2 blocks shorter. You’ll get that way two times the set G+L shown on the right of the above picture.

  2. Assembling the H and X groups (not on crystal 7):


    Assemble (two times) one H group with one X group by inserting in the cut outs of each H piece (example shown above by the blue rectangle) and L2 piece a set of F pieces whose base has a length being two blocks shorter than the H/L one (example shown in blue above; matches the blue part highlighted on the H5). You’ll get two sets H+X as shown on the right of the above picture.

  3. Inserting the G+L  groups on the main axis.

    Crystal15-S4 Crystal7-S4

    Place the C1 piece in front of you and cross a C2 over it as you can see above. Make sure that the C2 is aligned with the middle of C1. Take the structures created at step 1 from groups L and G. Take first the set that contains the standalone F1 (not the FK containing set). Those structures can be placed on the bottom part of C1 highlighted in blue in the picture above. To do this, rise C1+C2 so that C1 is vertical on your table and place the F1,L2,L3,etc on the bottom segment (thus, C2 is now blocked in position) to reach the state shown below.

    Crystal15-S5 Crystal7-S5

    Now take the second L+G set which contains the special FK this time. Place it similarly but on the top segment of C1 this time to reach the structure shown below. Comment: the special FK piece must be placed such as its cut out on C1 is oriented to the top. That way, the piece can slide higher on C1 (and following it all the L2, L3, L4 … ) by a length of a half block. To catch the idea, the moving blocks have been highlighted in blue in the next picture. The arrow shows the possible movement.

  4. Inserting of the last C2 axis.

    Crystal15-S6 Crystal7-S6

    Pick the last C2 axis and insert it as shown above, moving up the upper part of the structure. Take care that the cut out on the last C2 must fit itself in the remaining cut out of the C1 piece as shown on the crystal 7 picture (highlighted in red).

  5. Placing the F groups.

    Crystal15-S7 Crystal7-S7

    Take now the pieces of the two F groups and insert them vertically from the longest to the F1 along the C2 axis added in the previous step. Be careful as the bigger the crystal the more change something gets off balance and fall… zen and perseverance ! The next step will lock the struture as it is now.

  6. Placing the long F((N-3)/2) pieces out of group H.

    Crystal15-S8 Crystal7-S8

    Take the longest pieces out of the two H groups. Insert them one on each side – moving again first the upper structure – and place them all the way to the inner part of the structure as shown by the arrows. This will lock the added pieces in the previous steps in place.

  7. Placing of the remaining of the H+X groups.


    Insert now (on each sides) the structures built on step 2 from the pieces of groups H and X starting with the largest. To do that, proceed the same way as on the previous two steps: move up the upper part of the strucure (thanks to FK along C1) and insert the required structure on each side. Tips: 1. alternate the inserts. Do not insert all the structures on one side then all on the other side. Doing so would unbalance your crystal and increase the risk something falls. 2. insert the structures by pushing the continuous part of the Hx pieces on the outside. Doing so will ensure the vertical Fx pieces can’t move once the structure is pushed all the way to the center.
    Repeat this step to insert all the sizes of those structures, ending with the smallest standalone F1. (Comment: that’s the only action to be done for the crystal 7).

    Crystal15-S13 Crystal7-S13

    The crystal is now rebuilt.

  8. Locking the structure.

    Crystal15-S14 Crystal7-S14

    Don’t forget to rotate the FK piece by 90° as shown to lock the structure!

I hope you managed to get here without too much troubles !



1 Comment »

  1. Thanks a lot! I finally managed to get my crystal in one piece again!

    Comment by Hilke — June 8, 2010 @ 6:06 pm | Reply

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