Tie a Knot

First, get a completely untangled rope. Now, your task is to grab its two ends, and without letting it go, tie this knot in the middle.

In order to do this, first cross your arms, and from this position, grab the two ends of the rope. Once you untangle your arms, the knot will appear on the rope.

Donuts and Candies

Huey has 3 donuts, Dewey has 5 donuts. Louie comes along and the three of them split the donuts equally. In exchange, Louie offers 8 candies to Huey and Dewey. What is the fair way to split the candies?

Huey must take 1 chocolate, and Dewey must take 7. This is because each of them ate 8/3 donuts, and therefore Huey gave away 1/3 of a donut, whereas Dewey gave away 7/3 of a donut.

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.

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 wrongly placed;
  • 296 shares two digits with the number, but they are wrongly placed.

What is the number?

The first and second clues imply that the 6 is not a 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.