Floor Drawing 305: Solution

By Nathan Fung

Answer:
COLOR MICROGRAPHY

This puzzle consists of a description and the series of instructions similar to Sol Lewitt’s Wall Drawing 305. The puzzle title, the description, and the instructions themselves are meant to clue that these instructions should be applied on Sol Lewitt’s Bars of Colors Within Squares (MIT).

The instruction paragraphs come in two types: one where a series of numbered points are placed and one where lines are drawn using these numbered points. For each square of this artwork, solvers must take these instructions and find one paragraph of each type so that when the instructions are completed, three letters are drawn.

When the paragraphs have been assigned, the first letters of the paragraphs assigning the locations of the numbered points spell out `ADD TO FORM A CHAIN`

and the first letters of the instructions drawing the lines spell out `FIVE LETTER WORDS`

reading around the squares in counter-clockwise order.

The three-letter sequences are `ACA`

, `FFA`

, `IMB`

, `LDE`

, `EAL`

, `UFT`

, `ONI`

, `HAI`

, `ETR`

, `RAN`

, `OFE`

, `UMB`

, `TRI`

, `ATC`

, and `OLL`

; the orientation of these letters read so that the bottoms of the letters are on the outside of the artwork (so the first five read with the letter bottoms being on the left side).

Add a letter on either side of each three-letter sequence so that the letter added to the end of one sequence is the letter inserted before the next one forms the chain: `CACAO`

, `OFFAL`

, `LIMBO`

, `OLDER`

, `REALM`

, `MUFTI`

, `IONIC`

, `CHAIR`

, `RETRO`

, `ORANG`

, `GOFER`

, `RUMBA`

, `ATRIP`

, `PATCH`

, and `HOLLY`

. The letters added form the answer ** COLOR MICROGRAPHY**.

Approximate schematics of the floor designs along with drawn letters on top of them:

The first set of instructions in art order (first square being the upper left one):

- Assign as the first point the rightmost point where a yellow region and a green region meet. The second point is located at the rightmost point where a red region and a blue region meet. The third point is the midpoint between the lowest point where a green region and a blue region meet and the uppermost point of the green region that extends furthest down. The fourth point is located at the midpoint between the uppermost point where a red region and a blue region meet and the lowest point of the red region that extends furthest up. The fifth point is located on the green-blue edge that extends furthest left one-third of the edge’s distance from the right end of the edge. The sixth point is located on the red-yellow edge that extends furthest downward one-third of the edge’s distance from the top end of the edge. The seventh point is located where two red-blue edges meet. The eighth point is located where two green-blue edges meet.
- Designate the first point as the point located along the longest vertical red-yellow edge two-fifths of the edge’s distance from the bottom end of the edge. The second point is located along a vertical blue-purple edge one-fourth of the edge’s distance from the top end of the edge. The third point is located at the lowest blue point. The fourth point is located where the two longest yellow-bordering edges meet. The fifth point is located at a yellow-green-blue triple point. The sixth point is located at the uppermost red-yellow-blue triple point. The eighth point is located on the closest edge directly below a green-blue-purple triple point. The seventh point is located between the first and eighth point on an edge.
- Designate the first point as the point located on the rightmost orange-purple edge one-third of the edge’s length from the top end of the edge. The second point is located on a green-purple edge one-fourth of the edge’s length from the right end of the edge. The third point is located at the green-blue-purple triple point. The fourth point is located at the uppermost point of the lowest orange region. The fifth point is located on the leftmost red-purple edge one-third of the edge’s length from the bottom end of the edge. The sixth point is located at the red-orange-green triple point. The seventh point is located along two red-green edges.
- The first point is located at the yellow-green-blue triple point. The second point is located at the leftmost point of the blue region that extends the furthest right. The third point is located where two green-blue edges meet. The fourth point is located at the red-green-blue triple point. The fifth point is located at the midpoint of the leftmost green-blue edge. The seventh point is located on the nearest green-bordering edge left of the fourth point. The eighth point is located at the red-yellow-green triple point. The sixth point is located above the seventh point the same distance as the fourth point is from the eighth point.
- On this attempt, the first point is located at the lowest point where a green region and a purple region meet. The second point is located at the uppermost point where a red region and a purple region meet. The third point is located at the uppermost point where a red region and a yellow region meet. The fourth point is located at the uppermost point where a yellow region and a purple region meet. The fifth point is located on the longest red-yellow edge left of the midpoint of the rightmost red-blue edge. The sixth point is located on the red-yellow edge left of the first point. The eighth point is located on the red-green edge one-third of the edge’s length from the left end. The seventh point is located on a red-bordering edge so that it is collinear with the sixth and eighth points.
- For this attempt, the first point is located at the lowest point of the orange region that extends furthest up. The second point is located at the lowest point of the red region that extends furthest up. The third point is located at the rightmost point of the orange region that extends furthest left. The fourth point is located at the midpoint of the orange-green edge that extends furthest left. The fifth point is located where two orange-blue edges meet. The sixth point is located at the midpoint between the lowest point where a red region and a purple region meet and a point where two red-green edges meet. The seventh point is located at the closest blue-bordering edge below the lowest point on the edge of a purple region.
- On this attempt, the first point is located at the rightmost point of the green region that extends furthest left. The second point is located at the uppermost blue point. The third point is located at the midpoint of the yellow-green edge that extends furthest left. The fourth point is located where two orange-blue edges meet. The fifth point is located at the midpoint of the orange-green edge that extends furthest right. The sixth point is located at the rightmost point of the green region that extends furthest down. The seventh point is located at the midpoint of the orange-green edge that extends furthest left.
- Refer to the rightmost yellow point as the first point. The second point is the midpoint of the longest yellow-bordering edge. The third point is located below the leftmost point of the purple region that extends furthest right; it is located at the nearest edge below the aforementioned point that borders a green region. The fourth point is located between the second and third point on an edge that borders a yellow region. The fifth point is located on the longest orange-purple edge and is one-third of the edge’s length from the left end of the edge. The sixth point is located at the leftmost point where an orange region and a purple region meet. The seventh point is located at the leftmost point where a red region and a purple region meet.
- Make the first point the orange-green-purple triple point. The second point is the leftmost point of the purple region that borders the smallest green region. The third point is directly right of the first point on the nearest edge. The fourth point is located at the leftmost point where an orange region and a green region meet. The fifth point is located at a point where two edges bordering the same two colors meet; it is located directly to the left of a yellow-blue edge. The sixth point is located at the nearest triple point below the fourth point. The seventh point is located on the edge right of the sixth point; it is one-fourth of the edge’s length from the right end of this edge.
- Assign as the first point the leftmost point where a green region and a purple region meet. The second point is located at the rightmost point of the purple region. The fourth point is located on the orange-green edge one-fourth of the edge’s length from the left end. The fifth point is located on the red-orange edge collinear with the second and fourth points. The sixth point is located on an orange-green edge one-fifth of the edge’s length from the right end. The seventh point is located on a red-orange edge one-fifth of the distance from the right end. The eighth point is located at the lowest red-orange-yellow triple point. The third point is on the red-green edge collinear with the first and eighth point.
- Call the first point the point that is on the longest red-yellow edge two-fifths of the edge’s length from the bottom end of the edge. The second point is on a yellow-blue edge two-fifths of the edge’s length from the bottom end of the edge. The third point is located at the leftmost point where a green region and a purple region meet. The fourth point is located on the longest red-yellow edge one-fifth of the edge’s length from the top end of the edge. The fifth point is located at the uppermost point where a yellow region and a blue region meet. The sixth point is located at the uppermost point where a green region and a blue region meet. The seventh point is located at the lowest point where two red-yellow edges meet.
- Here the first point is the lowest point where a red region and an orange region meet. The second point is located on the orange-yellow edge that is parallel to an orange-blue edge one-fifth of the edge’s length from the bottom end of the edge. The third point is located at the midpoint of a red-yellow edge. The fourth point is located at the lowest point where a red region and a purple region meet. The fifth point is located at the uppermost purple point. The sixth point is located at the uppermost point where an orange region and a yellow region meet. The seventh point is located at the lowest point where an orange and purple point meet. The eighth point is located on the yellow-blue edge directly above the fifth point.
- Assign as the first point the point where two orange-purple edges meet. The second point is located at the lowest point where an orange region and a blue region meet. The third point is located at the midpoint of the yellow-purple edge that shares a point with the longest green-purple edge. The fourth point is located on the lowest blue-purple edge below the second point. The fifth point is located at the leftmost point where the green region that extends furthest right meets a blue region. The sixth point is located where two blue-purple edges meet. The seventh point is located above the first point half of the distance from the first point to the nearest edge above it. The eighth point is located on an orange-purple edge right of the uppermost point where an orange region and a green region meet.
- In this attempt, the first point is located at the lowest point where a red region and a yellow region meet. The second point is located at the midpoint of the orange-blue edge that extends furthest left. The third point is located at the yellow-green-blue triple point. The fourth point is located on the midpoint of the green-blue edge that extends furthest upwards. The fifth point is located below the fourth point collinear with the first and second points. The sixth point is located at the midpoint of the yellow-blue edge that extends furthest upwards. The seventh point is located at the midpoint of the red-green edge that extends furthest upwards.
- Now, the first point is located at the midpoint of the rightmost yellow-green edge that is above an orange-green-blue triple point. The second point is located at the point where two yellow-blue edges meet. The third point is located on the orange-yellow edge that extends furthest down one-third of the edge’s length from the left end of the edge. The fourth point is located at the uppermost point of the orange region that extends furthest downwards. The fifth point is located on the yellow-blue edge that extends furthest left and is one-third of the edge’s length from the left end of the edge. The sixth point is located at the midpoint of the yellow-purple edge. The seventh point is located above the sixth point and to the right of a yellow-blue-purple triple point. The eighth point is located where two yellow-green edges meet and is also above a previously drawn numbered point.

The second set of instructions in art order:

- First, draw a line left from the first point ending directly below the seventh point. Draw a line from the first point to the nearest even-numbered point. Draw a line left from the second point ending directly above the seventh point. Draw a line down from the third point until it reaches the nearest edge. Draw a line up from the fourth point until it reaches the nearest edge. Draw a line down from the fifth point until it reaches an edge bordering a blue region. Draw a line left from the fifth point until it reaches the nearest edge. Draw a line from the seventh point to the uppermost numbered point. Draw a line from the sixth point up until it reaches a previously drawn line.
- In this attempt, draw a line from the first point to the nearest even-numbered point on a purple-bordering edge. Draw a line from the fourth point to the nearest even numbered point. Draw a line left from the fifth point ending at the point when the line would change color a second time. Draw a line down from the fifth point to the nearest edge. Draw a line left from the sixth point until it reaches a point that is directly above the seventh point. Draw a line from the sixth point towards the fifth point ending halfway between the fifth and sixth point. Draw a line up from the second point ending when reaching a previously drawn line. Draw a line up from the third point ending when reaching a previously drawn line. Draw a line from the seventh point down until it meets a previously drawn line.
- Visibly draw a line left from the first point until it reaches the nearest edge. Draw a line from the second point to each of the two nearest numbered points. Draw a line left from the third point ending at the point when the line would change color a second time. Draw a line left from the fourth point ending at the point when the line would change color a second time. Draw a line right from the fifth point ending at the point when the line would change color a second time; continue by drawing a line from this ending point to the lowest even-numbered point. Draw a line up from the sixth point ending when reaching a previously drawn line; continue by drawing a line from this ending point to the lowest odd-numbered point. Draw a line up from the seventh point until it reaches a previously drawn line.
- Execute this drawing by first drawing a line from the first point to the nearest point where two edges bordering the same two colors meet. Draw a line from the first point to the nearest odd-numbered point. Draw a line from the second point down to the nearest edge. Draw a line from the third point down to the nearest edge. Draw a line from the fourth point to the leftmost numbered point on a blue-bordering edge. Draw a line from the fifth point to the nearest numbered point on an orange-bordering edge. Draw a line from the sixth point down the same distance the line was drawn from the first point in the first sentence of this paragraph. Draw a line from the sixth point to the nearest even-numbered point. Draw a line right from the seventh point until it meets a previously drawn line.
- Let’s start by drawing a line from the first point right until it reaches a blue-bordering edge. Draw a line from the first point down until it reaches a blue-bordering edge. Draw a line from the second point to the midpoint of the red-purple edge that extends furthest upwards. Draw a line from the third point down ending at a point left of the point where two red-purple edges meet. Draw a line down from the fourth point until it reaches a red-bordering edge. Draw a line from the fourth point to the nearest odd-numbered point. Draw a line from the fifth point to the nearest numbered point on a green-bordering edge. Draw a line from the sixth point to the nearest even-numbered point. Draw a line from the seventh point upwards until it reaches a previously drawn line.
- Execute this drawing by first drawing a line from the first point to the nearest odd-numbered point. Draw a line from the second point to the nearest edge below the point; draw this line so that it is perpendicular to the edge that the line is being drawn to. Draw a line from the second point to the rightmost point of the red region that extends the furthest left. Draw a line from the third point to the nearest numbered point that is bordering an orange region. Draw a line from the fourth point to the furthest point bordered by a blue region and a purple region. Draw a line from the fifth point to the nearest orange-green edge in a direction that is perpendicular to the edge that is being drawn to. Draw a line from the sixth point to the nearest edge below the point; draw this line so that it is perpendicular to the edge that the line is being drawn to. Draw a line from the seventh point parallel to the longest orange-green edge so that it meets a previously drawn line.
- This time, draw a line from the first point down until it reaches a point bordering a green region. Draw a line from the second point to the nearest even-numbered point. Draw a line from the third point to the uppermost numbered point. Draw a line from the fourth point to the leftmost numbered point on a green-bordering edge. Draw a line from the fifth point up until it reaches the second nearest edge. Draw a line from the sixth point to a point where two yellow-green edges meet. Draw a line from the sixth point to the second-nearest numbered point. Draw a line from the seventh point to the nearest odd-numbered point.
- This time, draw a line upwards from the first point until it reaches the nearest edge bordering a green region. Draw a line from the second point to the leftmost point where a yellow region and a green region meet. Draw a line from the third point to the second-nearest even-numbered point. Draw a line left from the fourth point until it reaches the nearest edge. Draw a line down from the fifth point ending at the point when the line would change color a second time. Draw a line down from the sixth point until it is directly left of the second point. Draw a line right from the seventh point until it reaches a previously drawn line.
- Execute this drawing by first drawing a line from the first point to the midpoint of the longest green-purple edge. Draw a line from the second point to a point where two orange-blue edges meet. Draw a line from the second point to the uppermost point where a green region and a blue region meet. Draw a line from the third point to the orange-green-blue triple point. Draw a line from the third point right until it reaches a previously drawn line. Draw a line from the fourth point one-third of the distance to the point where two orange-green edges meet. Draw a line from the fifth point to the nearest orange-yellow-green triple point. Draw a line from the fifth point one-third of the distance to the second-closest orange-yellow-purple triple point. Draw a line from the sixth point one-fourth of the distance towards the nearest point where two orange-purple edges meet. Draw a line from the seventh point up until reaching a previously drawn line.
- Right now, draw a line from the first point to the lowest point where a red region and a purple region meet. Draw a line from the first point to the nearest even-numbered point. Draw a line from the second point to the midpoint of the orange-green edge. Draw a line from the third point to the uppermost point where a green region and a purple region meet. Draw a line from the third point to a point on the red-orange edge one-fifth of the distance from the left end of the edge. Draw a line from the fourth point to the uppermost purple point. Draw a line from the fifth point in the direction of the seventh point stopping when reaching a previously drawn line. Draw a line from the sixth point to the nearest numbered point. Draw a line from the sixth point perpendicular to the edge that it is on until it reaches the nearest red-bordering edge. Draw a line from the seventh point perpendicular to the edge that it is on until it reaches the nearest green-bordering edge.
- We will draw a line right from the first point until it reaches the nearest green-bordering edge. Draw a line from the first point to the midpoint between the first and fourth point. Draw a line up from the second point the same distance as the line was drawn in the previous sentence. Draw a line left from the third point until it reaches the nearest red-bordering edge. Draw a line down from the third point until it reaches the nearest red-bordering edge. Draw a line from the fourth point to the nearest point where two edges bordering the same two colors meet. Draw a line right from the fourth point to the nearest green-bordering edge. Draw a line down from the fifth point to a previously drawn line. Draw a line down from the sixth point to a previously drawn line. Draw a line up from the seventh point to a previously drawn line. Draw a line right from the seventh point to a previously drawn line.
- On this attempt, draw a line left from the first point ending at the point adjacent to an orange region and a yellow region. Draw a line right from the second point ending at the nearest edge. Draw a line right from the third point until it reaches the nearest blue-bordering edge. Draw a line from the third point to the rightmost numbered point. Draw a line right from the fourth point to the nearest blue-bordering edge. Draw a line up from the fifth point ending at the point when the line would change color a second time. Draw a line left from the fifth point to the nearest blue-bordering edge; continue by drawing a line from this ending point to the uppermost numbered point on the leftmost yellow region. Draw a line down from the sixth point to a previously drawn line; continue by drawing a line from this ending point to the rightmost numbered point on the yellow region that extends furthest right. Draw a line from the seventh point to the nearest even-numbered point. Draw a line up from the first point until it reaches a previously drawn line.
- Right now, draw a line from the second point to the nearest even-numbered point. Draw a line from the second point to the nearest odd-numbered point. Draw a line from the third point to the nearest point where two edges bordering the same two colors meet. Draw a line from the fifth point to the nearest numbered point on an orange-bordering edge. Draw a line from the sixth point to the nearest even-numbered point. Draw a line from the seventh point right until it reaches the nearest edge. Draw a line down from the first point until it reaches a previously drawn line. Draw a line left from the fourth point until it reaches a previously drawn line.
- Draw a line from the first point to the leftmost numbered point. Draw a line from the second point to the point where two red-blue edges meet. Draw a line from the third point to the nearest point where two edges bordering the same two colors meet. Draw a line right from the fourth point until reaching the nearest edge. Draw a line up from the fourth point to the nearest orange-bordering edge. Draw a line right from the sixth point to the nearest edge. Draw a line left from the seventh point until reaching the nearest edge. Draw a line up from the seventh point to the nearest orange-bordering edge. Draw a line down from the fifth point until it reaches a previously drawn line.
- Start by drawing a line from the first point left until it reaches the nearest edge. Draw a line from the first point to the nearest numbered point. Draw a line from the second point to the nearest odd-numbered point. Draw a line from the third point to the nearest even-numbered point. Draw a line from the fourth point to the uppermost point of the yellow region that reaches furthest downward and is also adjacent to an orange region. Draw a line from the fifth point to the nearest odd-numbered point. Draw a line from the sixth point left to the nearest edge. Draw a line from the seventh point to the nearest numbered point.