by Matt Gruskin
Problem:

This puzzle consists of a colorful image, similar to the images generated by Rainbow Smoke.

By performing a frequency count of the colors used in the image, and analyzing the results, the solver might notice the following things:

• Only the upper six bits of each color channel are ever used—the lower two bits are always zero.
• The number of pixels in the image (512 × 512 = 262,144) is the same as the number of possible colors that can be made using six-bit color channels (64 × 64 × 64 = 262,144).
• Most colors are used only once. Thirteen colors are used twice.
• Of all possible colors that can be made using six-bit color channels, only a few are missing, and the same number are missing as the number of colors that are used twice.

Generating the missing colors, and sorting them by their red components, yields the following RGB values (with the upper five bits of the green and blue components converted to letters, and the lower three bits ignored, as they are always zero):

Red Green Blue
8 N O
16 W X
24 O R
32 R G
40 B A
48 N D
56 S O
64 R T
72 B Y
80 D I
88 S T
96 A N
104 C E

Reading across and then down, this spells out the instruction NOW XOR RGB AND SORT BY DISTANCE.

Isolating only the colors that are used twice in the original image results in an image similar to the following (the image included in this solution has had its non-black pixels expanded to 3 × 3 boxes centered on the original pixels, for ease of viewing):

XORing the red, green, and blue components of each unique color together, converting the upper 5 bits of this value to a letter, and ordering by the pixel distances between the two (x, y) coordinates for each color (which are all integers, and multiples of 25) yields the following values:

Distance Red Green Blue XORed
150 112 224 136 C
175 32 88 56 H
200 32 160 168 E
225 224 24 104 R
250 40 72 240 R
275 16 144 72 Y
300 24 208 216 B
325 80 232 216 L
350 200 48 128 O
375 80 192 8 S
400 8 40 184 S
425 152 64 160 O
450 232 144 16 M

This spells the answer to the puzzle, CHERRY BLOSSOM.