Circle 12 05 (Lesson4) – We Solve Problems

Circle 12 05 (Lesson4)

Circle name: Circle 12 05
Lesson name: Lesson4
Starts at : 13.05.2020 12:00

Problems:

1.

Dissections (other) 11-13

Decipher the following rebus $\\$
$\\$
All the digits indicated by the letter “E” are even $($ not necessarily equal $)$; all the numbers indicated by the letter O are odd $($ also not necessarily equal $)$.

2.

Processes and operations , Theory of algorithms (other) 11-14

There are 6 locked suitcases and 6 keys for them. It is not known which keys are for which suitcase. What is the smallest number of attempts do you need in order to open all the suitcases? How many attempts would you need if there are 10 suitcases and keys instead of 6?

3.

Theory of algorithms (other) 11-13

48 blacksmiths must shoe 60 horses. Each blacksmith spends 5 minutes on one horseshoe. What is the shortest time they should spend on the work? $($ Note that a horse can not stand on two legs. $)$

4.

Theory of algorithms (other) 11-13

Decipher the following rebus. Despite the fact that only two figures are known here, and all the others are replaced by asterisks, the question can be restored.$\\$

5.

Puzzles 11-14

Decode this rebus: replace the asterisks with numbers such that the equalities in each row are true and such that each number in the bottom row is equal to the sum of the numbers in the column above it.
$\\$

6.

Puzzles 11-14

In the rebus in the diagram below, the arithmetic operations are carried out from left to right (even though the brackets are not written).
For example, in the first row “$** \div 5 + * \times 7 = 4*$” is the same as “$((** \div 5) +*) \times 7 = 4*$”. Each number in the last row is the sum of the numbers in the column above it. The result of each $n$-th row is equal to the sum of the first four numbers in the $n$-th column. All of the numbers in this rebus are non-zero and do not begin with a zero, however they could end with a zero. That is, 10 is allowed but not 01 or 0. Solve the rebus.
$\\$

7.

Equations of higher order (other) , Integer and fractional parts. Archimedean property 13-15

During the chess tournament, several players played an odd number of games. Prove that the number of such players is even.

8.

Processes and operations , Theory of algorithms (other) 12-14

A traveller rents a room in an inn for a week and offers the innkeeper a chain of seven silver links as payment – one link per day, with the condition that they will be payed everyday. The innkeeper agrees, with the condition that the traveller can only cut one of the links. How did the traveller manage to pay the innkeeper?

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