## Sum Skyscraper

Sum-Skyscraper 5×5 puzzle
I made this puzzle just before Christmas, and it’s been waiting on my desktop to be posted here ever since! Well, now it finally has been.

This is a Sum Skyscraper. Place the digits 1 to 5 once each into every row and column in the grid. Numbers outside the grid provide the total (i.e. sum) of ‘visible’ grid digits along that row or column, if you imagine each digit as a building of that many storeys. Taller buildings always obscure shorter ones. So, for example, a clue for 21354 from the top of such a column would be 10, since the 2, 3 and 5 are visible (the 1 and 4 are obscured by the 2 and 5 respectively), and 2+3+5 = 10.

## Christmas Star Sudoku

Sudoku Christmas Star puzzle
A Sudoku, in a star shape.

Just that. (Place 1-9 once each into every row, column and bold-lined 3×3 box).

## Bridge Mazes

I’ve recently been making some material for a book of kids’ mazes, and so I thought it would be fun to post a harder version of some of those puzzles here.

First-up, here’s a weave maze, so-called because the paths weave over and under each other. In this puzzle I’ve drawn narrow bridges where one path crosses over another.

If the first one is too easy for you, try the second! It needs to be printed full-page in order to have enough space to solve it.

Just enter at the top of the maze and follow paths until you exit at the bottom of the maze.

## Wraparound Numberlink

I’m currently working on a forthcoming book (The Mammoth Book of Brain Workouts, published next year in the UK by Constable & Robinson, and in the US by Running Press), and have been experimenting with something I wrote about briefly a few years ago but hadn’t really tried since – variants on Numberlink.

Numberlink puzzles have proved popular recently in various guises, including Flow Free and other apps on mobile devices such as the iPhone. There are quite a few such apps available, but none of them force a unique solution on the user (and generally the puzzles do indeed have many different solutions), which when you’re playing against a computer that grades you isn’t necessarily a problem since you can at least be marked correct/wrong automatically.

For a logic puzzle solver, such vague puzzles are perhaps a bit disappointing because you will reach a point during solving where you can’t eliminate any options because they may all be valid, despite being contradictory.

I’ve made a printed book of 200 of these Flow Free puzzles – you can get it from Amazon.com (currently \$5.36) or Amazon.co.uk (£3.95) – and they’re actually quite fun to solve despite the multiple solutions (not all the puzzles have multiple solutions, but some do). Unlike traditional Numberlink the puzzles include an explicit rule that every cell in the grid must be used, which eliminates a lot of potential solutions and means the puzzles usually require some thought.

Toroidal numberlink 6×6 puzzle

Toroidal numberlink 5×5 puzzle

But such multi-solution puzzles are not the kind of puzzle I usually post, so I’m going to stick to logic puzzles with unique solutions on this blog.

It turns out that if you allow lines on a Numberlink puzzle to wrap around one edge and come back on the other – so if a line goes off one end of a row or column it comes back on at the other end of the same row or column – that the puzzles get very difficult very quickly. In fact, even at 5×5 many such puzzles are very challenging. Once you get to 6×6, I have real trouble with them.

Here’s a 5×5 and a 6×6 puzzle for you to try. Let me know how you get on! There’s no explicit rule that every cell must be used – but as a hint I can tell you that they are anyway. There’s a unique solution to each puzzle.

## 101 Giant Sudoku series

I’ve recently launched a new series of ‘101 Giant Sudoku’ books, to cater for those who like their Sudoku to be considerably larger than normal!

You can see the entire series at PuzzleBooks.org (scroll to the bottom) or visit Amazon and search for “101 giant sudoku”.

There are currently 12 books in the series: 14×14, 15×15, 16×16, 18×18, 20×20, 21×21, 22×22, 24×24, 25×25, 28×28, 30×30 and 36×36.

The larger puzzles work just as you’d expected, so in Sudoku 36×36, for example, you must place 0-9 and A-Z into every one of the 36 rows, 36 columns and 36 6×6 boxes!

These puzzles are designed so they don’t need any advanced logic – just scan the rows and columns and boxes to see what’s missing and what can fit where.

All of the puzzles are designed with attractive 8-way symmetry patterns.

## Sum Skyscraper puzzles

Following-up yesterday’s Skyscraper puzzles, I thought I’d post a couple of Sum Skyscraper variant puzzles.

Sum Skyscraper 6×6 puzzle

Sum Skyscraper 5×5 puzzle

Sum Skyscraper puzzles are very similar to Skyscraper puzzles, so no number can repeat in any row or column and external ’skyscraper’ clues reveal information about the numbers in the main grid. In 5×5 puzzles place 1-5, and in 6×6 puzzles place 1-6.

Each number in the completed grid represents a building of that many storeys, and place the buildings in such a way that each given number outside the grid represents the sum of the number of buildings that can be seen from that point, looking only at that number’s row or column. A building with a higher value always obscures a building with a lower value, while a building with a lower value never obscures a building with a higher value. So the clue ‘6′ in a 5×5 puzzle would indicate that the buildings ‘1′ and ‘5′ can be seen (’5′ is always visible in 5×5 puzzles), so the solution to a row might be 15234.

## Skyscraper puzzles

I haven’t posted here for a while, but to celebrate the advent of reduced-clue skyscraper puzzles on PuzzleMix.com earlier today I thought I’d post a few Skyscraper puzzles here.

Skyscraper 5×5 2 puzzle

Skyscraper 5×5 1 puzzle

Skyscraper puzzles combine the no-repeat row and column constraints of sudoku with novel additional clues. In these 5×5 puzzles, place the numbers 1-5 once each into every row and column. Each number in the completed grid represents a building of that many storeys.

Place the buildings in such a way that each given number outside the grid represents the number of buildings that can be seen from that point, looking only at that number’s row or column. A building with a higher value always obscures a building with a lower value, while a building with a lower value never obscures a building with a higher value.

= “Skyscraper puzzles combine the no-repeat row and column constraints of sudoku with novel additional clues.  ”;
instr += “This book contains puzzles of size 5×5, 6×6 and 7×7.  In each respective case place the numbers 1-5, 1-6 or 1-7 once each”;
instr += ” into every row and column.  All of the puzzles in this book are sorted in order of increasing logical difficulty irrespective of size.\n\n”;
instr += “Each number in the completed grid represents a building of that many storeys.  Place the buildings in such a way that each given number”;
instr += ” outside the grid represents the number of buildings that can be seen from that point, looking only at that number’s row or column.”;
instr += ”  A building with a higher value always obscures a building with a lower value, while a building with a lower value never obscures a building with”;
instr += ” a higher value.  ”;
nameTxt.Text = “Skyscraper”;

## Sudoku Xtra 21

Sudoku Xtra 21 is now available, both as a PDF download to print yourself and also as a pre-printed book from your local Amazon store.  Follow the links on the Sudoku Xtra website to get hold of it in your preferred form.

Sudoku Xtra 21 is packed full of 144 top-quality logic puzzles covering a wide range of types. There is a particular emphasis on Sudoku and new varieties appearing for the first time in this volume include Quad-Max Sudoku, Anti-Knight Sudoku, Slashed Sudoku, Minus Little Killer, Product Frame Sudoku, Headless Worm Sudoku, Extra Region Windmill Sudoku, Non-Consecutive Diagonal Sudoku, Mystery Calcudoku Zero and a giant Trio 13-grid Samurai Sudoku.

The very first page features a large Arrow Samurai Sudoku, and other returning variants that were recently introduced to the series include Worm Sudoku, Quad Clue Sudoku, Offset Sudoku, Sudoku XV and Kropki Sudoku.

Not only that, but there’s Hanjie, Futoshiki, Hashi, Yajilin, Calcudoku, Dominoes, Hitori, Slitherlink and many more logic puzzles.

Pre-printed copies are on top-quality, 8.5×11 inch paper ideal for solving on, while download PDFs are designed to fit both A4 and Letter paper for printing.

## iPad, iPhone and other touch support on PuzzleMix

Just a quick heads-up that PuzzleMix, my site where you can play a wide range of puzzles online, now supports touch screen play for all of the number entry puzzles – so that’s Sudoku, Killer Sudoku, Futoshiki, Calcudoku, Skyscraper, Sudoku X, Kropki Sudoku, Killer Sudoku Pro, Jigsaw Sudoku, Consecutive Sudoku, Wraparound Sudoku, Sudoku XV, Killer Sudoku X, Odd Pair Sudoku and more.

It’s pretty darn awesome, even if I do say so myself!  It handles the screen touch events directly so it’s just as fast as running a native application on the iPad or iPhone. It also works on other devices.

## Sudoku Xtra 20

Sudoku Xtra 20 is out now, available pre-printed from your local Amazon or as a PDF to download and print yourself.

Issue 20 is packed with 151 puzzles, featuring many new Sudoku variants including Arrow Sudoku, Worm Sudoku, Anti-King Sudoku, Quad Clue Sudoku, Argyle Sudoku, Frame Sudoku, Little Killer Sudoku, Extra Region Pointers Sudoku, Offset Sudoku, a huge Odd/Even Samurai 13-grid Sudoku and more, plus the new varieties introduced in Sudoku Xtra 19 are back too. Tapa and LITS puzzles also return this issue, along with many existing favourites, such as Hanjie, Battleships, Hashi, Calcudoku, Slitherlink and so on. There’s a full list on the Sudoku Xtra magazines page.