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## Question

If you saw three shadows on three fence posts, one painted white, one painted blue, and one painted red, which shadow would be the darkest?

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The red one? Or is this a riddle?

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Depends on how you define "darkest shadow".

Perceptually, you might consider the darkest shadow to be the one with the greatest difference in brightness between the lit area versus the shaded area of the post. In that case, I would imagine that the post that appears brightest when it's in full sunlight would be the one that appears to have the darkest shadow, because there's more brightness to be lost by being in the shade.

On the other hand, you could instead compare the brightness of the three shaded areas to each other instead of comparing them to the lit areas of their post. And consider the fact that there's probably some ambient indirect light that will give a little illumination to the areas in the shade. Then the darkest shaded area will be on the post that appears darkest in normal light.

Then there's the issue of which color is brightest or darkest in full sunlight. Normally one would think that white is the brightest and either blue or red would be darkest, but it depends on the shade of paint, and perhaps the perceptual abilities of the observer (especially if they're color blind).

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plasmid's analysis is fairly complete. It begins with "depends on ... ," which is another way of saying the question can't be answered without more information than the OP gives. I will add to the information contained in the OP the assumption that the puzzle creator has fulfilled the burden of providing sufficient information for an answer to be reached.

I will take that to imply the posts are in an umbral shadow, rather than a penumbral shadow where ambient light, of unspecified spectral content, comes into play. For in that case all we would know with certainty is that the white post would be brightest. If the ambient had an orange cast, the shadow on the blue post would be darkest; if green, the red post's shadow would be darkest. To assume the puzzle is well posed, we rule out the circumstance under which these considerations would come into play: we assume that the OP's shadows are umbral.

The answer then is that the shadowed areas on all three posts are devoid of illumination: the shadows are all black, and thus equally dark.

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I am surprised that this was not meant to be a riddle but an actual question. I won't try to compete with plasmid or bonanova's fairly comprehensive answers, but here's the simple reasoning behind my initial guess.

I chose the red one because I heard that our atmospheric gases scatter blue light more than any other frequency of light. Since the red fence is the only one that doesn't reflect blue light, I figured that its shadow should be the darkest.

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I am surprised that this was not meant to be a riddle but an actual question. I won't try to compete with plasmid or bonanova's fairly comprehensive answers, but here's the simple reasoning behind my initial guess.

I chose the red one because I heard that our atmospheric gases scatter blue light more than any other frequency of light. Since the red fence is the only one that doesn't reflect blue light, I figured that its shadow should be the darkest.

Short and probably unneeded dissertation on color: Outdoor light comes from the sun and is essentially white. But as sunlight passes through the atmosphere it is scattered, especially in the shorter (blue) wavelengths. So the sky, which is not a light source per se, does not look black (as it does in space, away from our atmosphere.) Scattered simply means deviating from straight-line propagation from the source of light. This also explains reddish sunrises and sunsets: when the sun is near the horizon, direct sunlight must pass through more atmosphere to get to us, and more blue light is removed as it is scattered back into space. Hence the "blue planet." So direct sunlight is whitish overhead, producing ambient bluish light from the sky, and reddish when low in the sky, producing ambient reddish "sunset" light reflected from clouds. That's why ambient skylight (what's still present in a penumbral shadow of the sun) could preferentially augment the brightness of either the red post or the blue post.

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