CiSRA Puzzle Competition 2013 - Solutions

5D. Three Colours

The first step is to recognise that all the words on the right hand side are movie titles (mostly famous ones, though a few more obscure) with whitespace and the word "red", "yellow", or "blue" removed. Here's the list of movies:

beach		Beach Red
brickroad		YellowBrickRoad
cliff		Red Cliff
crush		Blue Crush
darkworld		Dark Blue World
deepsea		Deep Blue Sea
dorians		Dorian Blues
fever		Yellow Fever
hooksummer		Red Hook Summer
intheface		Blue in the Face
intothe		Into the Blue
mango		Mango Yellow
miamis		Miami Blues
nineteenroses		Nineteen Red Roses
oxfords		Oxford Blues
raisethelantern		Raise the Red Lantern
rockwest		Red Rock West
scorpion		Red Scorpion
sheworearibbon		She Wore a Yellow Ribbon
thebadgeofcourage		The Red Badge of Courage
thebellies		The Yellow Bellies
thecanvas		The Red Canvas
theclouded		The Clouded Yellow
themercedes		The Yellow Mercedes
therollsroyce		The Yellow Rolls-Royce
theroseoftexas		The Yellow Rose of Texas
thesbrothers		The Blues Brothers
theshark		The Yellow Shark
thewomanin		The Woman in Red
valentine		Blue Valentine
victoria		Red Victoria

The three colours represented in the movie titles are also shown on the paint palate and can be seen in the letter grid.

A reasonable expectation is that we are expected to fit the words to the grid, and finish colouring it.

With this in mind, you may start trying to fit words in straight lines on the grid and quickly discover this doesn't work. Take the letter V. The red V in the bottom right of the grid could fit "victoria" diagonally up to the left, but the blue V in the lower left corner can only belong to "valentine", and it doesn't fit with a straight or diagonal line of letters.

So, if the words are not in straight lines, what constrains them? Based on the observations about the letter V, perhaps it is the first letters. The first letter of each movie string can be uniquely placed on the grid with the appropriate colour.

Listing the letters in the grid by colour:

Red: nrcrhttbfesnhnrnsttsv
Yellow: tndtbsmeosttdtssfr
Blue: chtsidimsdaedsvoesd
Uncoloured: tatkokeea

The first letters of each supplied movie string are:

Red: bchnrrstttv
Yellow: bfmsttttt
Blue: cdddiimotv

Encouragingly, each first letter of the supplied movie strings is represented in the grid with a letter of the appropriate colour. The remaining letters in the grid once the first letters have been removed are:

Red: fenhnrnsts
Yellow: ndseodssr
Blue: hssaedses
Uncoloured: tatkokeea

The first letter constraint alone is insufficient to place the words in the grid. The next intuitive leap is to realise that the last letters of each string are also on the grid.

The last letters of each supplied movie string are:

Red: hfrsntnesna
Yellow: dronsdsesk
Blue: hdaseessse

Removing these letters from the remaining set reveals that all the last letters are also uniquely present, although in this case some have to be taken from the uncoloured set. There are some uncoloured letters left over:

Red:
Yellow:
Blue:
Uncoloured: tatkoe

Putting aside these left-over letters for the moment, we can start filling out the grid, with the working assumptions that each letter in a string has to be adjacent to the previous letter in a straight line, the colour has to match, and there can't be more than one letter in a single grid square. The red words "cliff" and "beach" can be unambiguously fit into the grid with these assumptions, as can sections of "victoria" and "mango".

From there, further logical deductions will place the words and reveal that in some cases letters are forced to overlap. There is only one case of letters of the same colour overlapping, but many cases in which red letters merge with blue, blue with yellow, and yellow with red.

The next intuitive leap is to colour these overlapping letters according to the appropriate mixes of paints: blue and yellow make green, blue and red make purple, and red and yellow make orange. Using paint colour mixing (subtractive mixing) as opposed to light colour mixing (additive mixing) is motivated by the paint palate shown in the puzzle and the fact that the coloured squares have been shown as physically painted on a sheet of paper.

This colouring reveals the green string "themile", the purple string "theroseofcairo", and the orange string "aclockwork". These correspond to movie titles involving the appropriate colour: The Green Mile, The Purple Rose of Cairo, and A Clockwork Orange.

There is also an area in the upper left of the puzzle that is still blank at this point, with the six remaining uncoloured letters "tatkoe". These letters turn out to be the first and last letters of these three newly revealed colour-related strings.

Similarly to the previous word-fitting step, the three new colour strings must now be fitted into the remaining squares. Each string has one intersection with its complimentary colour (green and red at the letter "m", orange and blue at the letter "r", purple and yellow at the letter "s"). From left to right, these combined letters form the string "MRS".

The final grid looks like this:

The combination of complimentary colours has different results depending on how the colours are being combined. It has already been determined that we are dealing with the subtractive colour mixing of paints (as opposed to the additive colour mixing of light). In subtractive colour mixing, the complimentary combinations of green/red, orange/blue, and yellow/purple would result in black, grey, or brown, depending on the details of pigments and mixing ratios. While someone knowledgeable about colour theory would say the answer is theoretically black, given ideal subtractive pigments, most people with practical experience in mixing real life paints would know that their glass of paint water ends up a muddy brown.

The correct answer is further motivated by the glass of brown water shown in the puzzle, and the fact that neither "Mrs Black" nor "Mrs Grey" are movie titles, while Mrs Brown is an Academy Award nominated movie starring Judi Dench. The answer is the movie title MRS BROWN.

Puzzle design notes:

This puzzle was inspired by the popular "Fill a Pix" (also known as "Paint By Pairs") puzzles. In those puzzles, one must connect pairs of identical (sometimes coloured) numbers by filling in the corresponding number of grid squares in a continuous line. These formed pictures.

I love that style of puzzle (I was playing an iPhone game called "Piczle Lines") and thought it would be interesting to do a version with words instead of numbers. And because I'm a movie buff, I figured I could use movie titles to get the colours. While it would have been possible to make a picture, I thought it would be more fun to make further movie titles. I wrote out "aclockwork", "themile", and "theroseofcairo" and started trying to fit combinations of the appropriate primary colours to them separately.

In retrospect, perhaps I should have used hexagons - it would have made construction a lot easier! It took an enormous amount of time to smash the six subsections together into a rectangular grid. I ended up creating a program in HTML and Javascript to make construction easier (the above image is a screengrab from my program). On the bright side, the difficulty of construction gave me confidence that it would be possible to solve without ambiguity (apart from a small unresolvable niggle with a red/blue letter "n").

The puzzle was originally presented to the test solvers as a simple grid graphic, not a photo with a paint palette and glass of water. Solution went well until the final step, where some test solvers insisted the answer to the final paint-mixing question should be black, not brown. Some argument ensued, wherein a different solver said words to the effect of, "Come on! Don't be so pedantically scientific. When you get real paints and you physically mix them together it always ends up brown!" We realised that this was the sort of question ("What do you get when you mix purple and yellow paint?") where someone with a strong scientific background could potentially insist on the theoretically correct answer (black) and overlook the practical real world answer that most other people would immediately get (brown). In other words the puzzle might have been harder for someone who knows the theory of colour mixing than for someone who doesn't! To provide some assistance for those highly educated people, the puzzle presentation was changed to show physical paints, and the glass of brownish water. :-)

Special thanks to Geoff Bailey and David Karlov for their exemplary work in test solving.