“The Password Game” is a new web puzzle/game by Neal Agarwal, a Brooklyn-based software developer, popular for various fun projects hosted on his website Neil.Fun.

pon opening the game webpage, you are given the seemingly simple task of creating a password. The password, in order to be strong enough, needs to satisfy a list of conditions. The first few of them are common; there is a minimum length and special characters should be included. However, after complying with every rule on the screen, a new one appears, more complex and bizarre than the previous one. This forces you to constantly make changes to the increasingly lengthy password, while trying to resolve any conflicts that appear.

The Password Game is quite difficult. On our first try, we failed the game after not giving in a timely manner a bug emoji 🐛 to a chicken emoji 🐔 inside our 70+ character password, while simultaneously looking for a YouTube video of the exact runtime of 19 minutes and 34 seconds. Hopefully, you can do better.

If you enjoy “The Password Game”, you can take a look at Neil’s other creations, such as “The Absurd Trolley Problems”, which offers sinister twists on the famous Trolley Problem.

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!

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.

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

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

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

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

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:

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.

Pay attention to the last digit. If it is 5, then the number is composite (unless it is =5).

Check whether the sum of the digits is divisible by 3. If it is, then the number is composite (unless it is =3).

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!

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:

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.

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.

“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.

Vincent Bal is a Belgian writer and director. Apart from making movies, he is also famous for his art project Shadowology which combines everyday items, their shadows, and doodles, into one amazing collection of cartoons. If you want to see more of Vincent, you can follow him on Instagram, where he regularly posts new work.

Seeing Theory is a beautifully designed website, which aims to educate people about probability theory via series of visual and interactive lessons. If anyone is struggling to grasp some of the basic concepts in this field of mathematics or is just getting into it, the website can be a very useful learning tool. Seeing Theory was designed by Daniel Kunin as an undergraduate project in Brown University and has won numerous awards. To visit the website, click the banner below.

Our friends at Geek_X, an Australian company for high-quality geek stuff, recently created a fun interactive puzzle hunt. To solve it, visit the link from the video below…

Joseph Herscher is a kinetic artist and a YouTube personality, who specializes in creating intricate Rude Goldberg machines out of everyday objects. Some of his most popular machines are “The Page Turner”, “The Dresser”, and “The Cake Server” which you can see below. Joseph has been sharing his inventions on YouTube for more than 10 years, and you can explore all of them on his official channel. Who knows, maybe he will inspire you to start making fascinating Rude Goldberg machines as well!

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