## Friday, December 7, 2012

### A Tale of Two Painters

An ancient story goes that there was a king that wanted his reception hall to be painted and promised a bag of gold to an artist who will make the best wall-size creation.  Only two artists in the kingdom dared to participate. They were each assigned a long wall, opposite to each other.  One of the artists worked three days and three nights and made a magnificent full-wall drawing. Another artist slept most of the time, didn't request any paint and late third night installed a wall-size mirror.

The day of the show came and the king entered the hall observing two identical wall-size paintings. The hall had dim illumination so no reflection was visible. Still, the king was smart enough to recognize the fraud. He ordered a bag of gold to be brought in and placed next to the real painting. "You have created a masterpiece and this bag is yours," proclaimed the king to the first painter.
"Here is your reward," said the kind pointing to the reflection of the bag on the second painting.

The question is, how did the king know that the second painting is not real if he didn't approach either of them.

This is how the hall looks like right now, with both all-size paintings covered by drapes.

Your thoughts and ideas accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Ilya said...

Assuming the king stood right in the middle of the hall while he was looking at the two walls, what he saw in the mirror was a smaller version of the other wall (with the real painting) plus a lot more surrounding details, like the windows above the other wall. If he looked straight, he should have seen himself too. This is because of the way the light travels as it gets reflected by the mirror and reaches the eyes of the observer, with angle of incidence equal to angle of reflection. I am a little confused by the statement that "no reflection was visible" since if that were the case, then nothing would be seen in the mirror? The real painting seen there, as well as the bag of gold, were reflections, which means that "some" reflections were visible after all.

Dennis (of Dennis and Katrina) said...

Looking at the picture, there are differences in the left and right sides of the hall. For example, on the left, there is a bench between the dais and the white alcove; there is no bench in the corresponding place on the right.

When looking at the "mirror" picture, the King realized the hall details were wrong, and that it was a mirror.

Tom said...

The king may have been told by someone, or figured it from the given clue of no request for paints. The king may have recognized the fatigue of the first artist (the winner). But this is math puzzle.

If NO reflection was visible, how did the king observe two wall-size paintings? But evidently some reflection was indeed visible (the king saw SOMETHING), and the king saw his own reflection, on only the mirrored wall.

Anonymous said...

I am not sure what you mean that the king could see see a reflection but he did see two paintings. If he could see two paintings, then there must have been some reflection to see the mirrored one. Assuming he could see the "painting on the mirror", then the mirrored one would be smaller than the original. I would also think the mirrored side would be lighter since mirrors tend to collect light.

Gurubandhu

Jerome said...

So far, all I can think of is a right/left confusion. A mirror image will make left into right and right into left.

If there is any writing on the original (including signatures), it will come out backwards on the mirror image.

Anything that has a left and right to it (flags perhaps -- especially if the stripes are vertical) would be backwards.

Annie said...

Since the king was not actually in front of the mirror he was looking at it from an angle. The angle he was viewing it from and the reflection of this angle are equal so he was actually seeing something beyond the painting, maybe a familiar looking window or doorway! Wish I could make a diagram for you.......a picture is worth....well, you know! I hope my explanation is clear!

Jerome said...

Another fact. Wouldn't the image of the image (since it is virtual) appear to be the same distance behind the mirror as the object is in front? That couldn't be if there were two paintings, could it?

Anonymous said...

There was enough light in the hall for some reflection, such as the reflection of the money bag that was placed in front of the real painting. The king could tell which painting was real because the mirror side contained images such as of the person who placed down the money bag and of the other people in the hall at the same time (such as the artists, for example) that the real painting did not.

Even if hall was too dim for much reflection, the mirror side might still show a little bit of movement from the king and his entourage entering the hall (the curtains for the paintings rustling in the breeze for example), that a close observer could still tell the difference.

Maria said...

Oho-ho all together we have more answers than any of us thought.

First of all a clarification - by "no reflections" I meant no strong external light reflections (windows, ceiling lamps) that immediately reveal any mirrored object.

The answer I had in mind and most of you listed is that king passed in-between the paintings and suddenly noticed that one of the paintings contained him, a xeroxed him, a moving him, wait... a reflection of him. It is a mirror!

Another one that came in mind just now is that by some reason a large drape was put in-between the paintings, parallel to them and suddenly... one painting disappeared while the other stayed put.

But you came up with a few more interesting observations -
when viewed from an angle mirrored painting is smaller and will contain pieces of furniture from the room. Xeroxed (R-L flipped furniture) that may hint on reflection.

Mirrored painting will make room appear larger as painting on it will appear inside on the same depth as the width of the hall, extending the hall. Thinking about it, it may be actually a great idea to place such a large mirror in any room you are wishing to be larger. You get double art and double space (perceptually). Plus, you can save on light, windows and benches:)

A puzzle point for everyone who posted: Ilya, Dennis, Tom, Gurubandhu, Jerome, Annie and TracyZ.