False Statements

None of these statements is correct.
At most 1 of these statements is correct.
At most 2 of these statements are correct.
...
At most 98 of these statements are correct.
At most 99 of these statements are correct.

How many of these statements are correct?


If the number of true statements is X, then statements 1, 2, ... , X are wrong, and the rest are correct. Therefore X = 100 - X and X = 50. Thus, there are 50 correct statements.

Fidget Cube

Have you ever been solving hard problems and felt the need to fidget during the thinking process? Most of us use to click pens or spin keychains around our fingers, and this usually help us to maintain our focus. However, with the introduction of the Fidget Cube, Antsy Labs raises the fidgeting routine to a whole new level. The Fidget Cube is a novelty mechanical toy, which has a different item to play with on each of its faces. One face has a (non-)light switch which clicks, another has a joystick which glides, a third one has a little disc which spins, and I personally love all of them.

The Fidget Cube comes at a somewhat hefty price of $20-25, but as a toy you will find yourself constantly play with, I think it is definitely worth the money. You can also find cheaper knock-off versions of it on Amazon and other retailers, but they provide inferior quality, which I did not like.

Fidget Cube
  • fidgeting toy
  • good quality
  • novel idea
  • highly recommended

Balloon in a Car

balloon-1762994_1920.png

You are sitting in a motionless car, which is tightly sealed, i.e. no open windows, holes in the car, etc. A helium balloon on a string is tied to the floor. If you start accelerating the car, is the balloon going to move back, forward, or stay in place?


The reason the balloon floats up in the air is that the helium has lower density, so when gravity pulls the denser air around down, the ballon gets pushed up. Similarly, when the car accelerates, the air around gets drawn to the back of the car, which makes the helium ballon go forward.

Mastermind

You must find a 3-digit number. You know that:

  • 682 shares one digit with the number, and it is well placed
  • 614 shares one digit with the number, but it is wrong placed
  • 296 shares two digits with the number, but they are wrong placed

What is the number?


The first and second clues imply that the 6 is not part of the number. The third clue then implies that 2 and 9 are parts of the number. Now the first clue implies that 2 is the last digit of the number, and the third clue implies that 9 is the first digit of the number. Finally, the second clue implies that 4 is the second digit of the number.

Therefore, the number is 942.

Space Traffic

Help the police hunt down the red robot on the run. On the way, try to find:

  • one red-domed roof;
  • two yellow-capped chimneys;
  • three red-rimmed chimneys;
  • a sky scraper with four triangle-topped roofs;
  • a road that branches into five paths.
CLICK TO PRINT MAZE

CLICK TO PRINT MAZE

Labyrinth: Find your way through 14 magical mazes
By Theo Guignard
Published 2nd March by Wide Eyed Editions
ISBN: 9781847809988



The Evolution of Trust

During World War I, peace broke out.

It was Christmas 1914 on the Western Front. Despite strict orders not to chillax with the enemy, British and German soldiers left their trenches, crossed No Man’s Land, and gathered to bury their dead, exchange gifts, and play games.

Meanwhile: it’s 2017, the West has been at peace for decades, and wow, we suck at trust. Surveys show that, over the past forty years, fewer and fewer people say they trust each other. So here’s our puzzle:

Why, even in peacetime, do friends become enemies?
And why, even in wartime, do enemies become friends?
— The Evolution of Trust

Game Theory is an intriguing subject in Mathematics, with various real-life applications. Even though many people have heard about the "Prisoner's Dilemma" - one of the most famous problems in the field, few have delved deeper into the theory. Fortunately, Nicky Case (creator of "Parable of the Polygons") is here to help again, by educating us in a fun, engaging manner. Check out his quick, 30 minutes introduction to Game Theory by clicking the image below, and see if you can understand the questions proposed above any better.