# Introducing the 3D Connecting Wall!

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D.

A typical '2D' connecting wall puzzle (as made popular by the BBC quiz show, Only Connect) involves dividing a group of 16 seemingly unconnected words into four thematic groups of four, an activity which is represented by a 4x4 grid of squares.

This puzzle takes this to another dimension!

The diagram below depicts three adjacent sides of a 4x4x4 cube, each of which is its own 4x4 connecting wall comprising the faces of 16 smaller 'cubelets'. A pool of 37 words must be divided so as to form 12 thematic groups of four. Naturally, this means that - unlike in the 2D connecting wall - in a 3D connecting wall some words must appear in 2 or (in one case) 3 different categories at once! This can best be understood by imagining that each 'cubelet' in the diagram is assigned a word, which is written on each of its visible faces.

The three interconnected connecting walls are labelled T (top), R (right) and L (left), with each category (represented by the subscript numbers 1-4) being written out in the direction of the neighbouring arrow. For example, the elements of category T1 of the top connecting wall are shaded in red and appear along the northwest-southeast diagonal. Each of these elements also appears as an entry in one of categories L1 to L4 (three of which have been shaded pink) - and, in fact, the word to be positioned in the diagram's central cubelet (common to categories T1 and L1) further appears in category R1 also! The word to be placed in the central cubelet is omitted from the list of words provided and must be deduced in order to complete the puzzle.

You are provided with 36 of the 37 words to complete this 3D connecting wall, as follows:

APE ATLANTIS BANE BLUE BRAILLE BUSH
CAMERON CARTER COLUMBIA CUE DARTMOUTH DISCOVERY
ENDEAVOUR FORD GREEN JACKSON JOHNSON KENNEDY
LAKE LOWBROW LULU MAY MOLLY PEACOCK
PLUM POPEYE QUAYLE SCARLET SEE SONIA
STONE TEA URCHIN VEIL WHY YALE

If you require a structure for completing the diagram, perhaps the 'least chaotic' approach is to present elements 1 to 3 of each category in alphabetical order. One word (VEIL) has been positioned for you according to this style - the other words can be inserted around it. (You may or may not find this helpful.)

TASK: Position the 36 given words in this 3D connecting wall - one to a cubelet - in order to form 12 thematic groups of size four across the three visible sides of the full cube (in the directions of the given arrows). Discover the hidden word (not provided here) which should be positioned on the diagram's central cubelet, to discover what you get when you mix the red (T1), blue (R1) and yellow (L1) connected groups!

NB This puzzle type has the potential to be much more difficult than a standard connecting wall puzzle - both to solve and to set. All efforts have been made to try and ensure that a unique solution arrangement of clearly defined categories exists.

This is the evil genius of connecting walls, and the missing word is:

BROWN

And the groups are: (with the group-of-groups entry in each list bolded):

T2-4:

US Space shuttles:
ATLANTIS
DISCOVERY
ENDEAVOUR
COLUMBIA

Words that end with a part of the face:
POPEYE (eye)
URCHIN (chin)
LOWBROW (brow)
DARTMOUTH (mouth)

Words that rhyme with "ale":
QUAYLE
BRAILLE
VEIL
YALE

R2-4:

Former US presidents
(Jimmy) CARTER
(George) BUSH
(John F) KENNEDY
(Lyndon B) JOHNSON

Vegetable anagrams:
LAKE (kale)
BANE (bean)
APE (pea)
MAY (yam)

Oscar winning directors:
(Oliver) STONE
(John) FORD
(Peter) JACKSON
(James) CAMERON

L2-4:

Single word (mononymous?) UK Eurovision performers
SONIA
LULU
MOLLY
BLUE

Cluedo suspects:
(Miss) SCARLET
(Mrs.) PEACOCK
(Professor) PLUM
(Reverend) GREEN

Letter homophones:
WHY (Y)
SEE (C)
TEA (T)
CUE (Q)

T1:

This takes one word each from L1-4, to create:
Snooker balls:
BLUE
GREEN
CUE
BROWN

R1:

This takes one word each from T1-4, to create:
US Ivy League universities:
COLUMBIA
DARTMOUTH
YALE
BROWN

L1:

This takes one word each from R1-4, to create:
Former UK Prime Ministers:
CAMERON
MAY
JOHNSON
BROWN

And finally:

There is a hint in the task instructions to find what you get when you mix red, blue and yellow. And the answer to that (at least for pigments) is brown.
(This was (of course) only spotted in hindsight, well after I had the solution.)

• Excellent work, well done! Thinking in 3 dimensions in this puzzle is trickier than it seems at first... It also makes me now realise that for a unique presentation, having just one prefilled word isn't sufficient - it needs a second on another face. Thanks for the great answer - I might see if I can get this to work a second time too...
– Stiv
Jun 26, 2023 at 6:04
• @Stiv There is a whole bunch of symmetry in these puzzles. The groups are not ordered so one could switch say T3 and T4 on the diagram. Similarly one can switch the entire L side with the entire R side. But this doesn't actually change the solution in any way so there is no need to provide more prefilled words. Nice puzzle. Jun 26, 2023 at 6:58
• @quarague Precisely. That's why I specified the paragraph (below the 6x6 word list) about ordering elements 1-3 alphabetically in each group - once you do that (and provide a second placed element), the whole thing has a unique presentation!
– Stiv
Jun 26, 2023 at 7:34
• very nice puzzle, I'm starting to wonder what a 3-D connecting wall with traces of grid deduction and happy stars would look like :-) Jun 28, 2023 at 5:23