Problems

There are some incorrect weighing scales, a bag of cereal and a correct weight of 1 kg. How can you weigh on these scales 1 kg of cereals?

Michael thinks of a number no less than \(1\) and no greater than \(1000\). Victoria is only allowed to ask questions to which Michael can answer “yes” or “no” (Michael always tells the truth). Can Victoria figure out which number Michael thought of by asking \(10\) questions?

Deep in a forest there is a small town of talking animals. Elephant, Crocodile, Rabbit, Monkey, Bear, Heron and Fox are friends. They each have a landline telephone and each two telephones are connected by a wire. How many wires were required?

In a room, there are 85 balloons – red and blue ones. It is known that: 1) at least one of the balls is red, 2) from each arbitrarily chosen pair of balls at least one is blue. How many red balls are there in the room?

There are 6 locked suitcases and 6 keys to them. At the same time, it is not known to which suitcase each key fits. What is the smallest number of attempts you need to make in order to open all the suitcases for sure? And how many attempts will it take there are not 6 but 10 keys and suitcases?

If the Humpbacked Horse does not eat or sleep for seven days, it will lose its magical powers. Suppose he did not eat or sleep for a week. What should he do first of all by the end of the seventh day – eat or sleep, so as not to lose powers?

Decipher the following rebus (see the figure). Despite the fact that only two figures are known here, and all others are replaced by asterisks, the example can be restored.

Among some number of mathematicians, every seventh is a philosopher, and among some number of philosophers every ninth is a mathematician. Who are there more of: philosophers or mathematicians?

Know-it-all came to visit the twin brothers Screw and Nut, knowing that one of them never speaks the truth, and asked one of them: “Are you Screw?”. “Yes,” he replied. When Know-it-all asked the second brother the same question, he received an equally clear answer and immediately determined who was who.

Who was called Screw?

Uncle Jack, the cat Whiskers, Spot and postman Pat are sitting on a bench. If Spot, sitting to the right of everyone, sits between Uncle Jack and the cat, then the cat will be at the extreme left. In what order do they sit?