Puzzle 86: Scarcity

Pure Loop Loop: Draw a loop that passes all white cells and no black cell such that the loop goes horizontally or vertically at all times and never touches or crosses itself.

Expected difficulty Easy • Answer • Comment/E-mail if you want a solution to be published

Puzzle 86: Scarcity
Pure Loop
(click to enlarge)

Page 12 of Chessics #12 states that a 8×8 Pure Loop puzzle only needs four black squares to assure uniqueness of the solution, and page 143 of The Games and Puzzles Journal #8-9 states that with an addition of rows and columns (and black squares), the solution can be extended. However, I don’t find anything about how many extra black squares are necessary, so here I’ll give an upper bound: a Pure Loop needs at most black squares to ensure a unique solution. In fact, the result can be generalized to a rectangle: a Pure Loop needs at most black squares to ensure a unique solution (although obviously this is weak if is small compared to ). Is there anything stronger?

Puzzle 85: Loose Strands

Pure Loop Loop: Draw a loop that passes all white cells and no black cell such that the loop goes horizontally or vertically at all times and never touches or crosses itself.

Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published

Puzzle 85: Loose Strands
Pure Loop

There we go, the last of the series. Of course, the blog is turned off again for the moment, at least until I manage to construct more puzzles. I’m busy too, you know. (By the way, expect things.) Answer key would be “lengths of horizontal segments in row/vertical segments in column” for R1/C2 (or R2/C1 or something).

Another difficult “opening”. Also for some reason I find sudden interest on Pure Loop and Heteromino now, like exploring two untouched lands… (Okay, I think I see it being used in more things now, but still.) Did you know that Heteromino almost got into FAST (as an uninteresting 3×3), but Deb decided it was too obscure and got replaced with Kakuro, which in turn also got replaced by Next Term? The more you know.

Puzzle 84: Chopsticks

Hashiwokakero Draw some bridges connecting the islands (circles). Bridges can only run horizontally or vertically, and all islands must be connected (it must be possible to visit any island by using the bridges). Bridges cannot cross each other. Between any two islands, there may be at most two direct bridges connecting them. A number on an island gives the number of bridges connected to that island.

Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published

Puzzle 84: Chopsticks
Hashiwokakero

Because “hashi” can mean “chopsticks”. Fourth of the rejected series for FAST. The answer key would be “write 1 for every single bridge and 2 for every double bridge that crosses/goes along the marked rows”, with the two bottom rows as marked.

This is probably hard because you need to observe for the opening, a bit like the dreaded Hitori. Afterwards, I’d put it no more than a medium. And I hate making Hashi’s solution image; just check that answer when you’re done or something and guess how I made it.

Puzzle 83: Division

Star Battle Put two stars in each row, column, and region bounded by bold borders. A star occupies a cell, and no two stars are adjacent.

Expected difficulty Medium • Answer • Comment/E-mail if you want a solution to be published

Puzzle 83: Division
Star Battle

Third in the reject series. There was Star Battle in the original draft of the puzzle, and it’s not that trivial to solve the second part. (Of course, the answer key would be “enter the column number of the leftmost star in each row”.)

Also, apparently I start to construct puzzles on my computer too, instead of using my book again. This is what happens if you have too much access to computer. (Compare: a year ago I’m still at school, without computer access, hence why I use the book to store my puzzles.)

Puzzle 82: 5×10

Heyawake Dynasty-style: Shade some cells black so that no two black cells are orthogonally adjacent and all white cells are connected. A number inside a black bordered region—a room—indicates the number of black cells in the room. A run of contiguous white cells in the same row/column cannot span over two room boundaries.

Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published

Puzzle 82: 5×10
Heyawake

Second rejected puzzle. As you can guess, some of the top rows would have become the answer keys, and the bottom part I still can’t figure out a logical solution for.

Three more to come. Also the ordering of how these puzzles appear is determined indirectly by Yoshiap, whose I simply asked “give a permutation of 1,2,3,4,5”. 😛

Puzzle 81: Fell from the Sky

Skyscrapers Latin square: Put a number between 1 and 7 into each cell inclusive such that each row and column contains exactly one instance of each number. If we consider the numbers as heights of buildings, each number outside the grid tells the number of buildings visible from that point, looking into the grid. For example, an observer to the left of the sequence 1426375 sees four buildings (1,4,6,7; other buildings are hidden by taller buildings to the left).

Expected difficulty Medium • Answer • Comment/E-mail if you want a solution to be published

Puzzle 81: Fell from the Sky
Skyscrapers

This is the first in the series of the rejected puzzles for FAST, a joke test for April Fools Day. As described in a post in the discussion thread, my initial idea was “normal-sized” puzzles (even though I actually had 12×12’s and not 10×10’s), but with answer keys that are trivial to obtain. This, in some cases, lend to actually trivial puzzles too, but I don’t really like that, and hence here’s a handpicked collection of puzzles that I deem to be interesting enough even with the trivial answer key restriction. (Thus the title follows; the puzzles are those that “fell from the sky”, failed to be picked for the party.)

From The Archives 001: Symmetric–

This puzzle originally appeared in Deception, as the Bottom puzzle of Elimination Tapa.

Elimination Tapa Nurikabe-style: Shade some of the cells black. Black cells must be connected, but no 2×2 square may be all black. Cells containing numbers may not be shaded black. A cell with numbers represents the lengths of contiguous black cells in the cells adjacent to itself, separated by at least one white cell between different groups.

In addition, each square with numbers has one extra number. Removing extra numbers is part of the puzzle. Question marks indicate unknown numbers.

Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published

From The Archives 001: Symmetric–
Elimination Tapa

Clearly intended to be a standalone post for this.

Yeah, reposting puzzles I’ve published somewhere else. This includes my old blog.

Also, yay, managed to disable anti-aliasing with a program!

Puzzle 80: Hardcore Mode

Counting Count the number of paths from S (start) to G (goal) that stays along the white roads. Paths cannot use the same road twice but may visit the same intersection twice. As an example, the pink path shows one valid path.

Expected difficulty Insane • Answer • Comment/E-mail if you want a solution to be published

Puzzle 80: Hardcore Mode
Counting

Erm. You may use a calculator or a program. (If you managed to program the solution, then you deserve the answer. I’m not responsible if you miscalculate when you’re multiplying large numbers by hand.)

This is a rejected puzzle of a set born out of a stupid idea. Why did I even think of this? The good news is I have a free Brilliant.org problem idea, and I can practice my programming skills.

Puzzle 79: Hidden Object

Expected difficulty Hard • For personal reasons, I decide not to release the answer/solution for this puzzle. Sorry 😦

Puzzle 79: Hidden Object
Nonogram
(click to enlarge)

Puzzle 78: Totally Not An Approval

Scrabble Example

Scrabble Put some letters into the grid. The words that can be read (a span of two or more letters, preceded and followed by either the edge of the grid or a blank space) must be listed on the right, and no other word can be formed. All letters must form a single connected region.

Expected difficulty Easy • Answer • Comment/E-mail if you want a solution to be published

Puzzle 78: Totally Not An Approval
Scrabble

So Prasanna asked me to testsolve a Scrabble puzzle, with a word bank that resembles a sentence but has broken grammar. I suddenly got the idea for this word bank (which, Prasanna, has a perfect grammar, even if it uses a slang (v.intr. definition #4) 😛 ), and quickly whipped this puzzle in head. Turns out it’s unique, so why not. It’s actually Easy-Medium or something, as it’s not that trivial, but heck whatever.

Aftermath: Prasanna went hyper.

Also I went on to replace Puzzle 5; nobody noticed “the second path goes nowhere” and “the second path leads to freedom” are two contradictory statements?