Circle 12 05 (Lesson2) – We Solve Problems

Circle 12 05 (Lesson2)

Circle name: Circle 12 05
Lesson name: Lesson2
Starts at : 13.05.2020 10:00

Problems:

1.

Mathematical logic (other) 11-13

In a vase, there is a bouquet of 7 white and blue lilac branches. It is known that 1$)$ at least one branch is white, 2$)$ out of any two branches, at least one is blue. How many white branches and how many blue are there in the bouquet?

2.

Theory of algorithms (other) 11-13

Decipher the following puzzle. All the numbers indicated by the letter E, are even (not necessarily equal); all the numbers indicated by the letter O are odd (also not necessarily equal).

3.

Theory of algorithms (other) 11-13

On an island live knights who always tell the truth, and liars who always lie. A traveler met three islanders and asked each of them: “How many knights are among your companions?”. The first one answered: “Not one.” The second one said: “One.” What did the third man say?

4.

Dissections (other) 11-13

True or false? Prince Charming went to find Cinderella. He reached the crossroads and started to daydream. Suddenly he sees the Big Bad Wolf. And everyone knows that this Big Bad Wolf on one day answers every question truthfully, and a day later he lies, he proceeds in such a manner on alternate days. Prince Charming can ask the Big Bad Wolf exactly one question, after which it is necessary for him to choose which of the two roads to go on. What question can Prince Charming ask the Big Bad Wolf to find out for sure which of the roads leads to the Magic kingdom?

5.

Theory of algorithms (other) 11-13

An investigation is being conducted into the case of a stolen mustang. There are three suspects – Bill, Joe and Sam. At the trial, Sam said that the mustang was stolen by Joe. Bill and Joe also testified, but what they said, no one remembered, and all the records were lost. In the course of the trial it became clear that only one of the defendants had stolen the Mustang, and that only he had given a truthful testimony. So who stole the mustang?

6.

Theory of algorithms (other) 11-13

In the language of the Ancient Tribe, the alphabet consists of only two letters: M and O. Two words are synonyms, if one can be obtained by from the other by a$)$ the deletion of the letters MO or OOMM, b$)$ adding in any place the letter combination of OM. Are the words OMM and MOO synonyms in the language of the Ancient Tribe?

7.

Mathematical logic (other) 12-13

In a race between 6 athletes, Andrew falls behind Boris and two athletes finish between them. Vincent finished after Declan, but before George. Declan finished before Boris but after Eric. Which order did the athletes finish the race in?

8.

Arithmetics. Mental maths , Mathematical logic (other) 12-13

This problem is from Ancient Rome.
$\\$ A rich senator died, leaving his wife pregnant. After the senator’s death it was found out that he left a property of 210 talents (an Ancient Roman currency) in his will as follows: “In the case of the birth of a son, give the boy two thirds of my property (i.e. 140 talents) and the other third (i.e. 70 talents) to the mother. In the case of the birth of a daughter, give the girl one third of my property (i.e. 70 talents) and the other two thirds (i.e. 140 talents) to the mother.”
$\\$ The senator’s widow gave birth to twins: one boy and one girl. This possibility was not foreseen by the late senator. How can the property be divided between three inheritors so that it is as close as possible to the instructions of the will?

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