## Solution: 1C. Free Image Market

We are given 30 pictures of various things, and 30 labelled boxes, apparently to put them in. A brief inspection will reveal that this task is complicated by the fact that almost all the pictures can legitimately be placed in multiple possible labelled boxes!

The identification of the pictures, running left to right and then down the page, plus their possible associations to the labelled boxes, are as follows:

Although the multifarious possibilities may seem daunting, a start can be made in assigning the pictures to boxes by noting that there is only one pig and only one building. Also, since the rugby ball does not match any other label, it must be the ball, meaning the football (or soccer ball) has to go elsewhere. Proceeding this way eliminates many possibilities and allows the boxes to be mostly filled.

There are a few unresolvable ambiguities just using this approach. These can be resolved by the next step of the puzzle - extracting a message using the numbers in the corners of the images. By using this number to index into the label of the matching box, we can build up a coherent message.

The message reads: PASSED THROUGH VALLEY OF AMBIGUITY.

This is a reference to a quotation by the philosopher and pioneering economist Adam Smith: "On the road from the City of Skepticism, I had to pass through the Valley of Ambiguity." A quick Internet search should find this without any problem. Adam Smith is also one of the pioneers of the economic philosophy of the free market, which provides a link to the title of the puzzle.

So the person who passed thorugh the Valley of Ambiguity, and the solution to the puzzle, is ADAM SMITH.

Addendum: Some days after the end of the competition, a puzzling botanist wrote to use to say that the vegetable I called a swede/rutabaga is in fact a kohlrabi, which is a stem, and not a root at all. Looking at pictures of various kohlrabi and swedes/rutabagas now, I'm not in any position to argue against a botanist, as I can't reliably tell them apart by appearance. I will say in my defence however that all of the websites where this royalty-free photo of a.... whatever-it-is is available state clearly that it is a "Fresh turnip isolated on white". I looked up turnips and swedes, and found them both to be root vegetables, with the distinction basically being that turnips are white while swedes are purple. So I assumed it must really be a swede. I hope my mistake is understandable in this context, and that the error didn't cause any problems for other solvers with botanical backgrounds.

### Puzzle design notes

This puzzle was inspired by a similar puzzle shared by an Internet correspondent. That was a smaller and relatively simpler puzzle, designed to be solved in a couple of minutes in the field by geocachers, to reveal a secret message to anyone who successfully located the cache in which it was concealed. For this puzzle, I took the basic idea of matching ambiguous pictures to labels, and expanded the complexity and ambiguity level substantially.

It was fun coming up with a set of images, most of which fit multiple categories that several of the other images also belonged to. I also decided the hidden message should refer to ambiguity, to continue the theme, and some searching uncovered Adam Smith's quotation. The message was constructed to contain a number of letters that produced a neat rectangular arrangement of pictures: 30 letters giving a 5×6 grid.

Then I had to cut my set of inter-related ambiguous pictures down to 30, making sure to pick categories that provided the letters necessary to spell out the message. This resulted in the loss of some fun images and categories. A picture of the planet Neptune had to go, as well as the category "Tennis" and pictures of a tennis ball and Venus Williams. There was also a square root sign, an image of a hydroxyl radical, and the category "Radical", for mathematics and chemistry fans, but the symbols were less visually compelling than photos, and it was tough thinking of another useful category for the hydroxyl.

In test solving there was a slight stutter when one solver recognised Dr Bunsen Honeydew and called him "Professor Honeydew", which everyone accepted without checking. So they never even considered him for the role of "Doctor", but this didn't actually cause a problem.

Some solvers expressed an aesthetic dissatisfaction at having to resolve the final ambiguities by considering the message, rather than entirely through the logic of fitting images to categories. My point of view is that the entire puzzle is about ambiguity, and that removing some of the ambiguity (which is in fact ultimately resolvable given all the information in the puzzle) would lessen the strength of the theme. There are also the issues that making all of the images resolvable purely by category fitting: (1) would have made construction more difficult, and (2) the resulting set would not be so tightly interlocked in overlapping categorisations, somewhat reducing the level of fun and puzzlement. So we stuck with the original test solving version.