## Review

LOK is a new original puzzle book, created by the musical and visual artist Blaž Gracar. It is his first published work in this domain and considering the attention to detail put into puzzle design, solutions system, and illustrations, I would say that’s an impressive start, and I am looking forward to his future endeavors.

The puzzle mechanics of LOK are quite innovative, and despite my long-time puzzle history, I cannot relate them to anything I have seen before. Each puzzle consists of a grid partially filled with letters and the goal is to black out all cells by marking certain words and then triggering their effects. For example, if one has the letters L, O, K in consecutive cells and marks the resulting word LOK, then they must black out the cells of all three letters plus an additional cell by choice.

There are 5 more trigger words that appear in the book, but since it is the solver’s challenge to figure out what their effects are, I will not spoil them for you. All I can say is that each of them works uniquely and sometimes solving the puzzles gives the feeling of planning ahead the moves of a chess game.

In addition to the funny-sounding trigger words, new chapters introduce various other mechanics, building upon the previous ones and making the puzzles progressively more complex. You will encounter ”conductors“ that let you connect separated letters, “clouds” that let you black out a given configuration of cells, and other interesting concepts.

The book is split into 12 parts: 8 chapters with a total of 80 puzzles, 2 expansions with 10 extra puzzles, Rules that explain all the concepts in the book that have been left to the solver to discover, and Solutions that provide the answers to all puzzles. The parts are separated by beautifully illustrated pages of cute worm-like creatures, called ”Loks”, performing various activities, such as flying in space or working in a factory, on 10 additional solvable grids. Of course, the author could assemble the book just with all the 100 puzzles inside, and it still would have been great, but that extra touch of art is what makes LOK even more special for me.

While the market is currently flooded with all kinds of derivative logic books filled with computer generated Sudokus and Kakuros, LOK differentiates itself as an ingenious passion project of someone who simply wants to contribute to the world of puzzling. You can get the digital version of LOK for free from the author’s website by clicking the button below. If you like, there you can also purchase the physical edition and solve the puzzles the way they are intended to be solved, with pencil and eraser on paper. For those who prefer to keep their puzzle books in immaculate condition, a transparent draw board is included in the package. Thanks!

• appropriate for all ages
• more than 90 carefully hand-crafted puzzles
• surprising mechanics taught through practical solving
• explained rules and solutions included

## GET LOK HERE

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## Review

With the huge success of real-life Escape Rooms all around the world, more and more puzzle manufacturers have been trying to recreate the experience with their solve-at-home kits. ThinkFun‘s latest offering, Escape the Room: The Cursed Dollhouse, is possibly the closest you can get to the real thing, so far.

The setup of “The Cursed Dollhouse” is quick and simple. Within a few minutes you get to build a cardboard model of a dollhouse, turn on the recommended soundtrack of creepy music, and light up a few candles to get into the right mood. Once you do this, you can start reading the story of the house and unravel its mysteries.

You begin the adventure in the living room, where you have to solve several puzzles, involving a broken bookshelf, a dusty carpet, and a spiderweb on the wall. Then, you make your way through the rest of the house: kitchen, bathroom, bedroom, until you get to the attic. Each of the rooms you visit contains multiple objects, including hidden ones, which you need to use in order to solve its three challenges. Once you solve a challenge, you get a cryptic symbol which you must enter in the “solution wheel”. Get the three symbols correctly and proceed to the next room.

As you progress, you will encounter various puzzles, including many mechanical ones. You will have to cut, fold, entangle, and do all kinds of fun activities. The puzzles are logical and satisfying to solve. There were one or two which my group found a bit confusing, but fortunately, ThinkFun has created a website, where players can get small hints without spoiling the entire puzzles. In the end, all participants were very happy with the time we spent playing together.

While the price of “The Cursed Dollhouse” is a bit steep, the game provides a lengthy and immersive experience which justifies the cost. It also can be replayed by another group of people using the provided printable forms from the official website.

• 1-4 players, 13 years and up
• over 30 puzzles to solve within 2.5 hours
• realistic small-scale Escape Room experience
• puzzles are re-printable from the official website

## GET ESCAPE THE ROOM HERE

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## Review

Topple is a new online magazine that can be printed out and solved with pen and paper, the old-fashioned way. The price of each issue is just a meager $1, and for that amount you get a PDF of about 10 pages and up to 20 puzzles. The authors of the magazine have put efforts to provide a large variety of puzzles, so that everyone will find something they like. There are interesting trivia questions, rebuses, grid logic puzzles, as well as some unique challenges I have never encountered before. The number of puzzles in the magazine keeps increasing with each next issue: Issue 1: 7 Issue 2: 7 Issue 3: 10 Issue 4: 10 Issue 5: 10 Issue 6: 12 Issue 7: 16 Issue 8: 18 Issue 9: 18 The quality of the puzzles keeps improving as well, as you can see from these two identical puzzles, second one of which has updated artwork. Before you purchase the magazine, you can take a look at the 4-page sampler we have provided below. If you enjoy the Topple puzzles as much as we do, we recommend you to get the latest issue and then keep buying the older ones in a reverse order. At just$1, it will be hard to find something that provides better value for the money.

• appropriate for all ages
• PDF booklet for easy printing
• about 10-20 puzzles per issue
• fun old-school vibes
• just \$1

## GET TOPPLE MAGAZINE HERE

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## Brain Drop Podcast

Brain Drop is a new puzzle podcast by Brian Hobbs, released on a (mostly) weekly basis. In each episode, Brian presents 3 new puzzles and shares the solutions of the puzzles from the previous week. He uses professional voicework, music, and sound effects, to set up the mood and make his show more entertaining. Click the banner below to check out Brain Drop and see if you can answer Brian’s latest set of puzzles!

## Is This Prime?

In the past few days, I, my friends, and a whole lot of Twitter people have been trying to beat each other’s scores in the game “Is This Prime?”.

The game itself is simple; you are shown random integers on the screen and you need to guess whether they are prime or composite. Since most presented numbers are between 1 and 200, after a couple of games, players naturally memorize them. However, this is a good opportunity for students to review some main number division rules.

1. Numbers that end with an even digit are divisible by 2. If the number formed by the last 2 digits of a number is divisible by 4, the original number is also divisible by 4. If the number formed by the last 3 digits of a number is divisible by 8, the original number is also divisible by 8.
• 536 is divisible by 2 because 6 is an even digit
• 1348 is divisible by 4 because 48 is divisible by 4
• 71824 is divisible by 8 because 824 is divisible by 8
2. Numbers that end with 5 are divisible by 5. Numbers that end with 25, 50, 75, or 00 are divisible by 25.
• 45 is divisible by 5
• 675 is divisible by 25
3. Numbers whose sum of digits is divisible by 3 are divisible by 3. Numbers whose sum of digits is divisible by 9 are divisible by 9.
• 144 is divisible by 3 because 1+4+4=9 is divisible by 3
• 1638 is divisible by 9 because 1+6+3+8=18 is divisible by 9
4. If the difference between the sum of the digits in odd places and the sum of the digits in even places is divisible by 11, the number is divisible by 11.
• 121 is divisible by 11 because 1+1-2=0 is divisible by 11
• 209 is divisible by 11 because 2+9-0=11 is divisible by 11
• 1628 is divisible by 11 because 1+2-6-8=-11 is divisible by 11
5. If the number before the last digit minus twice the last digit is divisible by 7, the original number is also divisible by 7.
• 161 is divisible by 7 because 16-2×1=14 is divisible by 7
• 371 is divisible by 7 because 37-2×1=35 is divisible by 7
• 1589 is divisible by 7 because 158-2×9=140 is divisible by 7

All the rules above apply in both directions, e.g. if the sum of the digits of a number is not divisible by 9, then the number itself is also not divisible by 9. There are more complicated rules that apply to larger numbers but the chances are you will never get to use them. If you are curious to learn more about them, go to the bottom of this article.

Once we know the main number division rules well, we are ready to play the game! Here are a few tips for getting high scores:

1. Memorize as many numbers as possible. Knowing the multiplication table up to 10×10, it should be easy to learn by heart whether each number up to 100 is prime or composite.
2. Pay attention to the last digit. If it is 5, then the number is composite (unless it is =5).
3. Check whether the sum of the digits is divisible by 3. If it is, then the number is composite (unless it is =3).
4. If the number is between 100 and 300, check whether the sum of the first and the third digits equals the second digit. If this is true, then the number is divisible by 11, and therefore it is composite. 209 is the only other number in this range divisible by 11.

Good luck playing and let us know if you beat our personal record of 67 points!

### Primes between 1 and 300:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

### Sneaky composites:

51, 57, 87, 91

119, 133, 161, 169

209, 217, 221, 247, 253, 259, 287, 289, 299

## Some Math

Some of you may be wondering why the rules listed above work and whether we can create similar rules for larger numbers. Here are some explanations for the curious among you:

#### Rule for division by 3

Consider the 5-digit number ABCDE. It can be written as:

ABCDE = 10000A + 1000B + 100C + 10D + E

Since 10000 = 3 × 3333 + 1, 1000 = 3 × 333 + 1, 100 = 3 × 33 + 1, and 10 = 3 × 3 + 1, we can see that:

ABCDE = 3 × (3333A + 333B + 33C + 3D) + (A + B + C + D + E)

Therefore, ABCDE is divisible by 3 if and only if (A + B + C + D + E) is divisible by 3.

#### Rule for division by 11

Consider again the number ABCDE. Since 10000 = 11 × 909 + 1, 1000 = 11 × 91 – 1, 100 = 9 × 1 + 1, and 10 = 11 – 1, we can see that:

ABCDE = 11 × (909A + 91B + 9C + D) + (A – B + C – D + E)

Therefore, ABCDE is divisible by 11 if and only if (A – B + C – D + E) is divisible by 11.

#### Rule for division by 7

Once again, consider the number ABCDE. Notice that it can be written as:

ABCDE = 10 × ABCD + E

Now, let us find a number X such that 10X gives remainder 1 when divided by 7. Such number is X = 5. Indeed, 5 × 10 = 50 = 7 × 7 + 1. Therefore, the following statements are equivalent:

• ABCDE = 10 × ABCD + E is divisible by 7
• 5 × ABCDE = 49 × ABCD + ABCD + 5E is divisible by 7
• ABCD – 2E is divisible by 7

#### Rules for division by 13, 17, 19, etc.

The idea of the rule for division by 7 can be applied to rules for divisions by higher numbers. For example, here is how we can find a rule for division by 13:

1. Find the smallest positive integer X, so that 10X – 1 is divisible by 13. Such number is X = 4. Note that ABCDE is divisible by 13 if and only if 4 × ABCDE is divisible by 13.
2. Rewrite 4 × ABCDE as:
4 × ABCDE = 39 × ABCD + ABCD + 4E
3. Conclude that ABCDE is divisible by 13 if and only if ABCD + 4E is divisible by 13.

As an exercise, try to deduce a similar rules for division by 17 and 19! Note that for 17, instead of finding X, such that 10X – 1 is divisible by 17, you may get a simpler rule by finding X, such that 10X + 1 is divisible by 17.

For deeper understanding of how division of integers works, we recommend our more enthusiastic readers to look into Modular Arithmetic.

The Puzzle TOAD is a website, created by four Carnegie Melon professors (Tom Bohman, PO Shen-Loh, Alan Frieze, Danny Sleator), where you can find a growing collection of ingenious math brain teasers. Unlike Puzzle Prime, The Puzzle Toad is targeted exclusively towards math and computer science majors. Students who are preparing for college Olympiads will find the problems particularly useful. Check out The Puzzle TOAD by clicking the banner below.

## Review

Minecraft: Magnetic Travel Puzzle (M:MTP for short) is a travel game by ThinkFun in which the goal is to arrange 3 types of objects, each coming in 3 different colors, in a 3 by 3 grid, such that certain conditions are satisfied.

As you progress through the 40 included challenges, the types of conditions you encounter become gradually more complex. While in the beginning you may be given all the colors of the objects with one clue and all the types of the objects with another, later on you need to analyze 5 or 6 clues at once, which makes the game more challenging and fun. That being said, at the hardest levels, M:MTP is still relatively easy, so experienced puzzlers will probably breeze through it within an hour or two.

At its core, M:MTP is identical to ThinkFun’s previously released Clue Master. Both games are presented in the form of magnetic notebooks, so they are easy to pick up and travel around with. The illustrations of the Minecraft edition are all based on the popular video game, so its fans may be particularly appreciative.

If you are looking for a casual puzzle to pass an hour or two on a road trip, then M:MTP would be a great choice. I only wish there were more challenges included, especially more difficult ones.

• 1 player, 8 years and up
• 40 challenges with increasing difficulties
• easy to transport and play on the go
• cool Minecraft based art
• most puzzles can be solved with a few simple techniques

## GET M:MTP HERE

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## The Boat

“The Boat” is a graphic novel adaptation of Nam Le’s book, presented as an immersive webpage experience by Matt Huynh. With beautiful artwork and stunning effects, the novel tells the story of a 16-year old Vietnamese refugee, embarking on a dangerous trip across the sea. Click the banner below and scroll your way through this captivating, moving, and harrowing tale.

Have you noticed all those fun and interactive logos Google prepares for various occasions, such as holidays, sports events, and birthdays of famous people? If you have missed any of them in the past or you want to check again some of your favorite ones, you can do it by visiting the Google Doodle archive.

## Review

Cat Crimes is a logic game by ThinkFun inspired by classic deduction puzzles. It consists of 40 challenges split into four difficulty groups.

Each challenge presents the player with a cat crime which they must solve. One of six items on a carpet has been ruined, and several clues written on a card point towards the cat which is responsible. The player must analyze each of the clues, as well as the models of the cats and the carpet (included in the box), and find the perpetrator. Even though the puzzles can be completed just as easily with pen and paper only, the inclusion of cardboard models makes the solving process much more fun. The beautiful artwork of the set and the sturdy cardboard additionally improve the experience.

The included puzzles are best suited for students in primary and middle schools, but older people can enjoy them as well. Overall, Cat Crimes is a wonderful twist on a traditional type of puzzle, and I highly recommend it.

• 1 player, 8 years and up
• 40 challenges, 4 difficulty levels
• a fun variation of a classic deduction puzzle
• beautiful models of cats and carpet

## GET CAT CRIMES HERE

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