## The most Liked puzzles

### The fifth number

MathematicsThe set of numbers 1,3,8,120 has a remarkable property: the product of any two numbers is a perfect square minus one. Find a fifth number that could be added to the set preserving its property.

### 50 coins

LogicOnce upon a time, a tsar was holding a reception and the Megamind was among the guests. The tsar decided to test how smart the Megamind was, took him into a dark room, and gave the following task: On the table in this room, there are 50 coins, exactly 10 of them are tails up. In the darkness, it is impossible to determine the sides of these coins. Touching the coins also does not help. The Megamind has to separate these coins into two groups so that the number of tails in both are equal. Can he do it?

### Two incense sticks

LogicYou have two incense sticks, that burn unevenly, and a lighter. Each will burn for an hour. How can you time 45 minutes using nothing but these tools?

### A forger

WeighingsA Megamind owns a mint with a 100 workers. Each day, he gives 1kg of gold to each worker, and each worker must make 100 coins (10 grams each). The Megamind learnt that one of the workers is a forger, he makes coins that are 1g lighter. How can Megamind determine the forger using only one weighing? The scales can determine the total weight, up to 100 kg.

### Obtain 24

MathematicsUsing numbers 1,3,4,6, and basic arithmetic operations (addition, subtraction, multiplication, and division) and parentheses, obtain and an expression that evaluates to 24. You may use only these numbers and only these operations. Every number should be used exactly once. Numbers cannot be concatenated, i.e. you cannot use 13 or 146.