# Albcell.R Guide

See below for instructions on how to play Albcell.R.

*Albcell.r *is the third version of the *Albcell *puzzle, after *Albcell.1 *and *Albcell.d*. It offers puzzle lovers a relatively quick, stripped-down daily brainteaser, rather than the more “luxurious” and artistic option offered by *Albcell.d*, which can be enjoyed over a relaxing weekend. The streamlined design enables you to get straight to the heart of the puzzle and arrive at the unique solution through a series of logical steps, while never losing sight of what it is that makes *Albcell *so fascinating and absorbing.

As you untangle the invisible connections between the numbers, the “atomic structure” of the puzzle – its secrets and fine detail – will gradually reveal itself to you. Multiply this by 99 and you will soon discover that the pleasure in *Albcell *lies also in the way in which the experience “builds” as more puzzles are solved …

Most puzzle books grade each puzzle at the start, but for me that approach spoils the element of surprise. It’s far more interesting to discover the puzzle’s many rabbit holes during the solving process itself, which is why I’ve given the ratings at the end of the book, alongside each puzzle’s solution. (As a side note, this also highlights one of the perceptual differences between *Albcell.r *and *Albcell.1*, which includes a meticulously calculated difficulty level.)

By developing three varieties of the same puzzle, I’ve been able to fine-tune it – and this is another of *Albcell*’s advantages. Its multidimensional quality makes it distinct from other number-placement puzzles, offering you many different techniques to sharpen your skills in various settings and situations.

You can try solving the puzzle in the fastest time (by deducing the odd and even numbers separately), or use it to enhance certain facets of intelligence – such as multitasking and concentration – by switching between odd and even. As with many intellectual pursuits, *Albcell*’s possibilities become clear to those who have fully grasped the depth of the subject!

That said, the underlying principle of *Albcell *is always the same:

*Albcell ***is composed of a 10 x 10 grid of alternating diamonds and circles. Each puzzle is divided into a number of cell groups, separated by distinct lines. Place the numbers between 0 and 9 once in each row, column and cell group, putting the odd numbers (1, 3, 5, 7, 9) into the diamonds, and the even numbers (0, 2, 4, 6, 8) into the circles. **

Now let’s review a few tips and techniques that can help you solve the puzzles in this book. To begin with, we’ll focus on just a few numbers. As you familiarize yourself with the techniques you need to solve *Albcell*, you’ll learn how to use them in any setting and, eventually, develop your own puzzle-solving skills.

Take a look at the following diagrams:

## Note

In the first diagram, the rows are denoted using numbers, and in the second the columns are denoted using letters. The third gives the corresponding notation for each cell. This will help us to identify specific cells as we proceed through the puzzle.

Now let’s try some examples to get started …

In each of the diagrams shown below, the question mark must represent the number 8. Why? Well, in diagram *a*, it’s clear that 8 is the only even number missing in row 1. Equally, the question mark in diagram *b *must be an 8, because it can’t be 0 (there’s already a 0 in column **i**, in cell *i3*). Again, in diagram *c*, the question mark can only be an 8, because 4 and 6 already appear in row 1, and 0 and 2 in column **i**. In diagram *d *the logic is the same: the question mark in *i1 *can only be an 8, because all the other even numbers in its corresponding row and column are accounted for.

Now let’s dig a little deeper … Study the numbers and their positions in the diagram below, then try to answer these queries about the cells containing question marks:

- Where can the number 4 fit in the marked cell group in the center? At first glance, it looks like it must be either
*e5*or*g5*. However, on closer inspection, it should become clear that the question mark is in*e5*for a reason … - What about the number 7 – should it be in
*i2*or*j1*? (Look at the highlighted cell group in the upper-right corner).

Take a moment to think about it, then check the answer.

The next diagram shows why the 4 must be in *e5 *and the 7 in *j1*. The black and grey lines indicate the cells we can safely ignore for even and odd numbers, respectively. The question mark in *e5 *has to be a 4 because every row and column must contain that number, and in this example, the 4 in *f4 *and the 4 in *d8 *cover off every other circle in column **e**.

We can apply the same logic to the 7 in *j1*. The 7 in *b9 *covers off b1, and *h1 *is excluded because of the 7 in *h5*. The 7 can’t be in the other two diamonds in that row, *d1 *and *f1*, because the cell group they belong to already contains a 7, in *f3*.

In the next diagram, can you deduce which numbers are in cells *b1 *and *i1*? Look at the highlighted cell groups. For the group on the left, the 1 in *a10 *covers off all the diamonds in columns **a **and **b **except cell *b1 *(because as well as being in column **a**, it’s also in the cell group that goes from *a10 *to *b2*). So by a process of elimination, *b1 *must contain a 1. Equally, in the cell group on the right, the 0 in *j10 *covers off all the circles in columns **i **and **j **except cell *i1*. So if you figured out that *b1 *is 1 and *i1 *is 0, then you were correct!$

We can apply the same logic to the 7 in *j1*. The 7 in *b9 *covers off b1, and *h1 *is excluded because of the 7 in *h5*. The 7 can’t be in the other two diamonds in that row, *d1 *and *f1*, because the cell group they belong to already contains a 7, in *f3*.

Now let’s consider a final example, which is slightly trickier. In the diagram below, look at the positions of the 7s in *b7 *and *c10. *Based on this information, where can you place a 7 in column **a**? Applying the “process of elimination” technique we used before, you should realize quite quickly that a 7 can be placed safely in *a2*.

However, we have some additional information that can be useful … Notice that the 7 in *i8 *covers off (among other things) the diamonds at *i6 *and *i4*, while the 7 in *b7 *means we can exclude a 7 from *j7*. This means that the 7 in that particular cell group can only go in *j5 *or *j3*.

But wait! The 7 in *c10 *can also be quite useful. By covering off *c4 *– and because *b3 *is covered off by *b7 *– the 7 in row 3 must be in *d3*, *f3 *or *h3*. This information helps us to conclude that there cannot be a 7 in *j3*, so the only remaining position for a 7 in that cell group must be *j5*. (Look at the next diagram to see what I mean.)

Incidentally, thanks to this latest discovery for *j5, *the position of the 7 in column **d **should also become clear … But I’ll stop there, as by now you should have everything you need to familiarise yourself with the puzzle.

One last thing, though – I want to highlight an important feature that can easily be overlooked. Look at the puzzle fragment below. Although all ten numbers are present, the numbers 4, 1, 3 and 0 are in the wrong cells – even numbers are in diamonds and odd in circles. As you rush towards the end of the puzzle, be sure not to make too many mistakes – always pay attention to the shapes as well as the numbers!

A final note: *Albcell *puzzles can be addictive – so enjoy responsibly!