Following-up yesterday’s Skyscraper puzzles, I thought I’d post a couple of Sum Skyscraper variant puzzles.
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.
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 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.
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.
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 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.
In Little-Killer Sudoku the total of each of the diagonals in the grid, other than those 9 cells long, is given. Each number has an arrow next to it which points to the diagonal it gives the sum of, so therefore the top-left cell in this grid must be a 9 thanks to the arrow immediately below and to the left of it. Unlike in regular Killer Sudoku, there is no restriction on repeating digits in any sum.
I’ve also seen Little Killer puzzles which have an additional restriction that no number can repeat on either of the two main diagonals, but I haven’t used that rule here, so numbers can repeat. Apart from the addition of the Little Killer clues, this is a regular Sudoku puzzle.
Probably because it sounded cool, or it was invented by someone who didn’t quite speak English, Killer Sudoku puzzles with some of the redundant clues removed are often referred to as ‘Zero’ Killer Sudoku. Or perhaps it’s because there are “zero redundant clues”. In any case, here’s one of those puzzles, where I have taken out all but the clues you definitely need to get a unique solution.
Usual Killer Sudoku rules apply: Place 1 to 9 in each row, column and bold-lined box as usual, but you must also ensure that each dashed-line cage adds up to the total given at the top-left of it. Numbers can not repeat in a dashed-line cage.
Speaking for myself, I found this puzzle really challenging to solve, but I can promise you that there’s no need to guess or use trial and error in any way – every deduction can be made using standard killer solving techniques.
This is a non-consecutive-diagonal sudoku puzzle. No digit may be diagonally-adjacent to a consecutive digit. But as you can see from the givens, consecutive numbers can be adjacent horizontally or vertically. What you can’t have, for example, is a 1 diagonally next to a 2 because the 1 & 2 are ‘consecutive’ (have a numeric difference of 1).
Here’s something a little different – a consecutive snake sudoku.
Each of the shaded snakes consists of only ‘consecutive’ cells along its length, which means that any two cells joined by a snake must have values with a difference of 1, such as 2&3 or 7&8. So for example the 4-square-long snake at the top-left might have 2323 along its length, or any valid fit such as that.
In addition follow usual sudoku rules. Also note that only the cells joined by the snakes have any special relationship – any other pair of cells may or may not be consecutive (unlike in regular consecutive sudoku).
I often post pretty challenging puzzles here, so I thought I’d entirely reverse that trend by publishing probably the easiest 9×9 puzzle with minimal givens you’ve ever seen.
Simply place 1-9 once each into every row, column and bold-lined region, as in a regular sudoku, but in this Odd/Even puzzle all of the even digits are in shaded cells. This is also a Trio sudoku too so each of the cells with an inset square contains 4, 5 or 6 and each of the cells with an inset circle contains 7, 8 or 9. Those without an inset square or circle contain 1, 2 or 3.
Using these rules you need only 3 givens for a valid unique puzzle. That’s the minimum number as you can probably easily convince yourself, because, despite its perhaps intimidating appearance, it’s essentially a set of trivial 1- and 2-digit sudokus laid on top of each other.