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# Reading List: ‘Absolutely Nasty Sudoku, Level 2’ (Frank Longo)

I enjoy logic puzzles (not just in a formal context, to be clear). Probably one of the most well-known genres of these is sudoku, a grid-based constraint satisfaction problem made popular by the Japanese publisher Nikoli. Given a 9 by 9 grid which may be decomposed into three 3 by 3 sub-grids (boxes), fill in numbers such that there is precisely one number from 1 to 9 in each row, column and 3 by 3 sub-grid. Some numbers are already given as clues; there is usually only one unique solution for a given clue set.

Solving a sudoku puzzle, in general terms, is NP-complete (of course, for a 9 by 9 grid, solving can be done in constant time). ‘Obvious’ strategies involve finding the only place in each row/column/box where a given number could go (since each of these must contain each digit once), or finding the only number that could be assigned to a given cell.

The next step would then involve considering interactions between cells – for example, ‘these two cells in this row can only contain 3 and 5, so no other cells can contain a 3 or a 5’, or ‘both of the cells where 7 could go in this box are in the top row, so there can’t be a 7 in the top row of the other two boxes that are horizontally aligned’ (called a pointing pair). Complexity only develops from there; there are a myriad of clever strategies as shown on the sidebar here.

Sudoku (sudokus?) are often featured in newspapers, and there are many compilations of these. However, as one gets familiar with the strategies, these can become less interesting. For example, consider this hard sudoku from the Guardian; a not-that-smooth solve yielded a 5m11s time, and the most complex technique I used was the ‘pairs’ reasoning I outlined above.

I recently discovered Frank Longo’s Absolutely Nasty Sudoku series, and thankfully this is one series which seems to live up to its name. Consider this grid (which is the puzzle above, converted into an easier to read format):

The grid pictured above is from a puzzle towards the tail end of the Level 2 book. Although no cells are obvious (and it doesn’t look like the pairs/triples logic yields anything), there are several ways to proceed from here:

• In row 3, you can have an 8 only in columns 2 and 9. This is also true in row 6. This means that no other rows can have 8s in columns 2 and 9; in particular, the second cell in the bottom-most row can’t be an 8, and has to be a 4. (This strategy is called X-Wing.) This is arguably the most straightforward deduction here, though it wasn’t the one I saw.
• Consider that if row 5 column 1 was a 5, then row 8 column 1 must be an 8; that forces row 9 column 2 to be a 4, and row 9 column 7 to be an 8. Alternatively, row 5 column 1 can be an 8. Either way, row 5 column 7 can’t be an 8, and must be a 4. (This strategy is called an XY-Chain.)
• Suppose row 6 column 7 was a 9. Then, the rectangle of cells with vertices in rows 1 and 3 and columns 4 and 7 admits two solutions; without affecting other cells, I can have either a 3 or 7 be in the top left corner. Thus, row 6 column 7 can’t be a 9, and must be a 3. (This strategy is called a Unique Rectangle.) This was actually the next step I made when solving this puzzle!

A key criterion when evaluating whether a Sudoku book (or a puzzle book in general) would be the difficulty and quality of the puzzles. The difficulty level for Level 2 is well-placed for someone like me, if maybe a little on the easier side; I’m familiar with most/all of the ‘basic’ techniques, and am aware of though not confident with trickier techniques like the aforementioned Unique Rectangle. I might have preferred Level 3, actually; there were several puzzles at the beginning of Level 2 that seemed like they could be solved with techniques I’d consider as basic. I also haven’t found any “broken” puzzles which couldn’t be solved (presumably, the author would have checked these with a solver before publication)!

I also have other criteria for evaluating Sudoku books, though. I tend to write down cell candidates as well as other annotations when solving. These help me more easily remember observations like pointing pairs; I’d prefer the grids to be sufficiently large that I can comfortably write these out. The grids in this book were certainly of adequate size. While my handwriting tends to be quite small, I don’t think grid size would be problematic for most people.

The choice of ring binding seems to make sense, too; the book needs to remain open when one is solving. Generally I found the paper to be very smooth to write on. I don’t have many complaints here.

The book has a very brief foreword, and then gets straight into the puzzles (with solutions at the back). The target audience is clearly people who are well-accustomed to Sudoku. As mentioned earlier, this is the second in a five-part series and based on online reviews I determined this to be a good place to start. I wouldn’t recommend this for someone just starting out with Sudoku, though.

# Reading List: ‘Misbehaving’ (Richard Thaler)

I spent a good amount of time thinking about whether I should register in the UK Registered Traveller Scheme (costs £70). In total, I easily spent more than seven hours thinking through this, modelling a few scenarios, and trying to estimate the value of my time relative to data about airport immigration queue timings. I earn more than £10 an hour.

In hindsight, I tried to make a good decision above, but the decision to try (at least as hard as I did) was probably a bad one. I’ve generally always been interested in making better decisions, and these decisions often involve managing resources that are finite. I’m not sure exactly when I first came across the field of behavioural economics, though. The notion of an Econ (a fully rational agent that maximises self-interest) is certainly something I’d come across in high school economics classes. I remember also familiarising myself with quite a number of these cognitive biases when attending talks on personal finance during various past internships – and certainly when reading up on personal finance online.

Misbehaving describes a wide variety of historical research events concerning behavioural economics. This covers its growth from infancy to becoming relatively widely accepted in the mainstream. While some rudimentary knowledge of mathematics is needed to follow the text, I wouldn’t say much background is required. I was fairly familiar with quite a large number of the experiments described, so I would imagine that there might not be that much new content for readers already interested in the field. Nonetheless, there were quite a few new things I came across; I hadn’t heard of the mug experiment [1] used to demonstrate the endowment effect. The analyses of closed-end mutual funds [2] and NFL draft picks were also interesting to read – it was nice to be able to relate knowledge to concrete application.

The book begins with an introduction to how the field came about, describing the author’s observations about human behaviour in practice that contradicted the true behaviour of a rational Econ. These include considering supposedly irrelevant factors (SIFs) like one’s current feelings as relevant; valuing things that one owns (one’s endowment) higher than things one could own, and an imbalance between preference for gains and losses. There was also a relatively more anecdotal list of observations the author made too. I’ve made my own list for things I’ve done in the past, and clearly do suffer from a number of these inconsistencies as well:

• The introductory example. (What’s the value of an hour?)
• The returns from my mutual funds come from both capital gains and dividends. So far at least, I’ve always been reinvesting all dividends. Yet, I feel happy when a dividend comes in. (Dividends are taxed more harshly than capital gains.)
• I’m much happier receiving a gift that someone has picked out for me than if the person gave me the cash and suggested that I might be interested in buying the gift with the cash. (I can replicate the first scenario in the second, and I also have more choices.)

From there, a variety of topics are presented in a largely topical and somewhat vaguely chronological idea. I think my complaint that I found a substantial portion of the material to already be familiar was largely in sections II (“Mental Accounting”) and III (“Self-Control”), perhaps because these are the relatively common examples people with some interest in the field are likely to come across first. The later sections get more interesting. Section VI (“Finance”) played well with my own interest in personal finance; Section VII (“Helping Out”) discusses practical applications of using insights from behavioural finance to ‘nudge’ people to make better decisions regarding their own finances… or complying with tax law.

The book ends with the author outlining hopes for how behavioural economics could continue to grow in relevance, discussing fledgling work in education. There is also an interesting section where the author dispenses some advice for life in general, based on his work in behavioural economics (specifically: make observations, collect data, and be willing to speak up).

While models should indeed account for important variables, I’m not sure I necessarily agree that these factors should be consistent over time, mainly because I think individuals can learn and within certain bounds optimise their own behaviour, though not to the point of being a hyper-rational Econ. Although in chapter 6 (“The Gauntlet”) it is claimed that learning how to make many high-stakes decisions is difficult because we don’t get many attempts at them, I think some of the decision-making skills are transferable. I might not get to make many decisions buying houses, and there certainly are aspects about buying a house that are peculiar to the task itself – yet, learning to learn about relevant considerations for the domain (as I already do with consumer electronics), plan how one’s cash flow is going to work (as I already do with regular investment into mutual funds) and being more aware of possible cognitive biases (relevant in almost all decisions) all seem to be helpful.

I enjoyed the book as a whole; it was a pretty engrossing read on my flight from Singapore to London. It held my attention for at least a good three or four continuous hours on that plane, and I was eager to finish reading the book when I landed in London. I’d recommend it as a good read, though as this is written to a fairly general audience readers who already have substantial knowledge of the field might find there not to be as much fresh content.