In the near future we will be adding a link here to “How to Solve Quip-BildTM Puzzles” – comprehensive suggestions about how to solve this new kind of word puzzle. In the meantime, what follows is a quick “short course” on Quip-Bild solving.
When you think that you have solved a Quip-Bild puzzle, the moment of truth – the real test of your proposed solution – is seeing whether it will actually fit onto the Quipto® diagram. It is easy to draw a diagram by first drawing a hexagon (a rough approximation will do) and then adding three intersecting pairs of chevron shapes inside the hexagon, like this:
This diagram represents a half-rack; think of it as a flat map of three faces of the cube, analogous to a flat map of one hemisphere of our globe. The solution to most Quip-Bild puzzles can be fitted within the three faces of a half-rack. Each position where a letter may be placed is called a cubicle, and cubicles are of three types: face cubicles, edge cubicles, and corner cubicles.
It is possible to solve a Quip-Bild puzzle by trial and error – writing letters into half-rack diagrams until you come up with an arrangement of letters that works to spell out the given quip as a continuous path on the diagram. However, there is a more systematic approach to solving, developed by the author/inventor over many years of experience with these puzzles. That approach is what we will briefly describe in what follows.
In our description of the solving process, we will be using the concepts of “links”, “chains”, and “poles”. A link is the connection between two letters that are adjacent anywhere in the quip; and a chain is a series of linked letters that connect two poles, letters in the quip that have been chosen because they have a number of connecting chains. These concepts will become clearer as we proceed.
As our example quip in these instructions, we have chosen the well-known proverb, “An apple a day keeps the doctor away.”
The first step is to make a link diagram: a spelling-out of the quip with dashes between the adjacent letters, where each letter is written only once. Here is a link diagram for “An apple a day keeps the doctor away”:
As you can see, to create a link diagram, you begin writing the letters of the quip in a circle (or, if you prefer, a more squarish arrangement), looping back whenever a letter recurs. Proceed carefully and try not to write any letter twice.
Having completed the link diagram (and perhaps double-checked it – it is frustrating to “solve” a Quip-Bild puzzle only to discover that, for example, your link diagram includes a repeated letter), the next step is to create a list of links – a listing of the letters that have three or more other letters adjacent to them in the quip, along with those adjacent letters. (We suggest circling the letters as you add them to the list.) Here is the link list for our quip, “An apple a day …”:
Next we look for potential “poles” – pairs of letters (usually letters that are among those with the greatest number of adjacents) that have, ideally, two or more “mutually-adjacent” letters (letters that are adjacent to both members of the pair). For example, in “An apple a day …,” the rather obvious choice of poles is the pair A and E; the two letters are adjacent to one another, they are the two letters with the greatest number of adjacents, and they have two mutual-adjacents, D and P.
Now we create a list of chains – all the chains linking the two selected poles, listed in order of length, shortest to longest:
(You may have noticed an apparent omission here: the chain AROCTHE. This is not an oversight; we recommend adding a chain only if it includes at least one link not involved in a previous chain listed, and all of the links in AROCTHE have already been accounted for in AROTHE and ADOCTHE.)
Finally, we try to fit the letters onto the rack. Here we take advantage of the fact that any two adjacent faces of the Quipto rack, if “flattened,” can be represented by a 3 x 5 grid, and letters that spell out the desired quip on a 3 x 5 grid can be placed on two faces the rack in the same arrangement.
So, starting with the shortest of the chains we have identified, we begin trying to place the chains of letters into a 3 x 5 grid pattern. The shorter chains tend to form a cluster around which the solver is challenged to add the longer chains.
We also take advantage of a crucial fact: the fact that the third face of the half-rack includes one position (the center cubicle, or “face cubicle”) that is adjacent to all of the cubicles along the edge of the 3 x 5 grid pattern of the other two faces. This fact is the key to many Quip-Bild solutions since that cubicle provides a “shortcut” across the third face.
After some trial and error, we come up with an arrangement that seems to work. Here is our solution, before we try to place it onto the rack diagram; note that in this solution, the letter O occupies that crucial “shortcut” position on the third face.
(One of the most critical factors in solving “An apple a day …” is the fact that 7 different letters must be adjacent to A. Since no more than 8 letters can be adjacent to any letter on the diagram, there is only one cubicle (letter position) adjacent to A that we can “waste”; in our solution, that position is occupied by K.)
Here is our solution placed on the half-rack diagram:
Finally, we must mention two related features of the Quipto rack that were not involved in our solving of “An apple a day …” but may be important in the solving of other Quip-Bild puzzles involving other quips. The first is the fact that along the edges of the 3 x 5 grid we have used in solving, every second cubicle will become a corner cubicle, and the cubicles on each side of a corner cubicle (edge cubicles) are adjacent to one another across the corner. Thus, for example, in the solution above, H and R are adjacent.
The second is the phenomenon of wraparounds, or hidden adjacencies; these involve edge cubicles around the periphery of a half-rack that do not appear to be adjacent in the diagram, but actually are – on the hidden back side of the rack. Thus, for example, in the solution above, K and L are adjacent.
We will treat these important topics at greater length in the full “How to Solve Quip-Bild Puzzles” instructions to come.
We hope that you enjoy solving Quip-Bild puzzles. We suggest starting with yesterday’s Quip-Bild puzzle: “Four score and seven years ago …”; see if you can hide this phrase on the Quipto rack!
And check our archives: The answer to any Quip-Find puzzle in this blog can serve as the given quip for a Quip-Bild puzzle.
— Jim Rader, inventor & puzzlemaster
Copyright © 2017 James E. Rader