Recently, the Acquisitions Editor of Brain Games, a publication in which I've been attempting to get published ever since the previous Acquisitions Editor contacted me a year ago, offered to send some free issues of Brain Games to help me get an idea of what kind of puzzles are offered. I graciously accepted the offer, and the issues arrived two days ago. The following are two puzzles called Digital Sudoku which appeared in issue 29. The instructions, as explained in Brain Games, are as follows: "Fill in the grid such that each row, each column, and each 2 by 3 box contains the numbers 1 through 6 exactly once. Numbers are in digital form. Some segments have been filled in." (These puzzles are © 2009 Publications International, Ltd.; I believe the use of just two puzzles from a past issue for review purposes qualifies as fair use, but will remove this post gladly otherwise.)

**WHAT FOLLOWS ARE SOLUTIONS AND SPOILERS. YOU MAY WISH TO SOLVE THE PUZZLES YOURSELF BEFORE YOU CONTINUE READING.**

It is common, especially when solving a difficult Sudoku, to start by placing "candidates" in every unknown cell, representing all of the digits that can possibly go in that cell, and then to logically eliminate candidates gradually until the puzzle is completed. This is the approach I will be using here.

Note: In these solutions, whenever a digit is placed, that digit will be removed as a candidate from elsewhere in the row, column, and block, without this being explicitly mentioned in the solution.

HS = Hidden single (out of all of the cells in a row, column, or block, only one of them can have a particular number)

NS = Naked single (only one number remains possible in a particular cell)

R2C3 means the cell in row 2 and column 3.

The first puzzle:

---456 1-3456 123456 | -23456 ---456 123456

-23-56 -23-56 123456 | ---456 ---456 123456

123456 1234-- 123456 | 1234-- 123456 1234--

-2---6 -23456 -23-56 | 123456 123456 123456

123456 123456 123456 | -2---6 ---456 1234--

1234-- 123456 1234-- | 1234-- 123456 -2---6

* The 5 in the lower-right block can only be at R5C5 or R6C5; either way, the rest of column 5 cannot contain another 5.

* R1C5 and R2C5 must be 4 and 6 in some order; the rest of column 5 and the rest of the upper-right block cannot contain another 4 or 6.

* R2C4 and R5C5 are 5 (NS).

* R4C6 is a 5 (HS in block). R6C2 is a 5 (HS in block).

* R4C4 is a 6 (HS in block). R6C6 is a 6 (HS in block).

* Row 4 can be solved completely by NS's or HS's; R4C1 is 2, R4C2 is 4, R4C3 is 3, and R4C5 is 1.

* Column 4 can be solved completely by NS's or HS's; R1C4 is 3, R3C4 is 4, R5C4 is 2, and R5C4 is 1.

* Column 2 can be solved completely by NS's or HS's; R1C2 is 6, R2C2 is 2, R3C2 is 1, and R5C2 is 3.

* Column 5 can be solved completely by NS's or HS's; R1C5 is 4, R2C5 is 6, R3C5 is 2, and R6C5 is 3.

* Column 6 can be solved completely by NS's or HS's; R1C6 is 2, R2C6 is 1, R3C6 is 3, and R5C6 is 4.

* The remainder of the puzzle can be solved by NS's. Solution:

561 342

324 561

615 423

243 615

136 254

452 136

The second puzzle:

123456 ---456 -2---6 | 123456 123456 ---456

123456 123456 -23456 | ---456 123456 123456

123456 123456 123456 | 123456 123456 123456

1-3456 ---456 123456 | ---456 1-3456 ---456

123456 -23456 -23-56 | ---456 1234-- 123456

123456 123456 -23-56 | 123456 123456 1234--

* R4C3 is a 2 (HS in row). R3C3 is a 1 (HS in column). R2C3 is a 4 (HS in column).

* R1C3 is a 6 (NS). R1C2 is a 5 (NS). R1C6 is a 4 (NS).

* R4C5 is a 1 (HS in block). R4C1 is a 3 (HS in row). R2C2 is a 3 (HS in block). R3C1 is a 5 (HS in block).

* R6C2 is a 1 (HS in column). R5C6 is a 1 (HS in block). R1C4 is a 1 (HS in block). R2C1 is a 1 (HS in block).

* R5C2 is a 2 (HS in column). R1C1 is a 2 (NS). R1C5 is a 3 (NS).

* Row 5 can be solved by HS or NS; R5C1 is 6, R5C3 is 3, R5C4 is 5, and R5C5 is 4.

* R4C6 is a 5 (HS in block). R2C5 is a 5 (HS in block). R6C3 is a 5 (HS in block).

* R2C4 is a 6 (NS). R6C5 is a 6 (HS in block). R3C6 is a 6 (HS in block). R4C2 is a 6 (HS in block).

* The remainder of the puzzle can be solved by NS's. Solution:

256 134

134 652

541 326

362 415

623 541

415 263

I can't say I have any complaints about these puzzles; they weren't particularly astonishing or amazing, but they were an enjoyable change of pace from regular Sudoku puzzles, and I had to use my brain to do them. What I do have a complaint about is their presentation -- specifically the difficulty grading system. Brain Games grades the difficulty of its puzzles on a scale of Level 1 (easiest) through Level 5 (hardest). The first Digital Sudoku above was graded a Level 3 puzzle, but the second one was graded a level 4 puzzle. I personally had a bit of an easier time solving the latter puzzle than the former. I see no way to solve the first puzzle without using a naked pair (as I did in the second step of my solution) or a naked triple, but the second puzzle was solved via singles alone. Why is the former puzzle one level easier than the latter? Do neuroscientists know something that I don't? According to Ryuta Kawashima, creator of the game Brain Age: Train Your Brain in Minutes a Day! (the creator of the recent brain-training bandwagon on which Brain Games jumped), the brain works harder when solving simple math problems quickly or reading aloud than when doing a difficult math problem. Is that same principle going on here? Do hidden and naked singles exercise the brain more than naked pairs? I'm really interested in knowing this.

As Brain Games is my potential future employer, I certainly hope that the criticism offered in this post will be taken constructively by my potential superiors.

## 1 comment

at 6*6 they are more boring than 9*9 mutants, but are rather boring no matter what ... as the possible cells replace the cool incomplete digits immediately and then its simple mini sudoku from there.

Ken's review: not worth the effort.

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