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Replace the letters in the word $TRANSPORTIROVKA$ by numbers $($different letters correspond to different numbers, but the same letters correspond to identical numbers$)$ so that the inequality $T >R > A > N < <P <O < R < T > I > R > O < V < K < A.$

Some girls are on a street. On the street, standing in a circle, four girls are talking: Janine, Mimi, Beatrix and Tash. A girl in a green dress $($not Janine or Mimi$)$ stands between a girl in a blue dress and Tash. A girl in a white dress is standing between a girl in a pink dress and Mimi. What dress is on each of the girls?

Professions of family members. In the Smith family there are 5 people: a husband, a wife, their son, a husband’s sister and the father of his wife. They all work. One is an engineer, another is a lawyer, the third is a mechanic, the fourth is an economist, the fifth is a teacher. Here’s what else is known about them. The lawyer and the teacher are not blood relatives. The mechanic is a good athlete. He followed in the footsteps of an economist and played football for the national team of the plant. The engineer is older than his brother’s wife, but younger than the teacher. The economist is older than the mechanic. What are the professions of each member of the Smith family?

We meet three people: Alex, Brian and Ben. One of them is an architect, the other is a baker and the third is an bus driver. One lives in Aberdeen, the other in Birmingham and the third in Brighton.$\\$

1) Ben is in Birmingham only for trips, and even then very rarely. However, all his relatives live in this city.$\\$

2) For two of these people the first letter of their name, the city they live in and their job is the same.$\\$

3) The wife of the architect is Ben’s younger sister.

Three friends were at the prom dressed in white, red and blue dresses. Their shoes were of the same three colors. Only Sarah’s shoes and dress were of the same color. Laura was wearing white shoes. Neither the dress nor the shoes of Linda were red. Identify the colors of the dresses and of the shoes of the three friends.

In the race of six athletes, Andrew lagged behind Brian and two more athletes. Victor finished after Dennis, but before George. Dennis beat Brian, but still came after Eustace. What place did each athlete take?

Teams A, B, C, D and E participated in a relay. Before the competition, five fans expressed the following forecasts.

1) team E will take 1st place, team C – 2nd;

2) team A will take 2nd place, D – 4th;

3) C – 3rd place, E – 5th;

4) C – 1st place, D – 4th;

5) A – 2nd place, C – 3rd.

In each forecast, one part was confirmed, and the other was not. What place did each team take?

A cube with a side of 1 m was sawn into cubes with a side of 1 cm and they were in a row $($along a straight line$)$. How long was the line?

The vendor has a cup weighing scales with unequal shoulders and weights. First he weighs the goods on one cup, then on the other, and takes the average weight. Does he deceive customers?

Among 40 containers there are two containers of different shapes and two containers of different colors. Prove that among them there are two containers that are both of different shapes and colors.

At the cat show, 10 male cats and 19 female cats sit in a row where next to each female cat sits a fatter male cat. Prove that next to each male cat is a female cat, which is thinner than it.

Two tribes live on the island: natives and newcomers. It is known that the natives always tell the truth and the newcomers always lie. A traveler hired an indigenous islander as a guide. On the way, they met a man. The traveler asked the guide to find out which tribe this person belongs to. The guide returned and said that the man said that he was a native. Who was the guide – a native or a newcomer?

Ten people wanted to found a club. To do this, they need to collect a certain amount of entrance fees. If the organizers were five people more, then each of them would have to pay £100 less. How much money did each one pay?

Decipher the puzzle: $KIS + KSI = ISK.$ The same letters correspond to the same numbers, different letters correspond to different numbers.

Try to get one billion $1000000000$ by multiplying two whole numbers, in each of which there cannot be a single zero.

Will the quotient or the remainder change if a divided number and the divisor are increased by 3 times?

A square piece of paper is cut into 6 pieces, each of which is a convex polygon. 5 of the pieces are lost, leaving only one piece in the form of a regular octagon $($see the drawing$)$. Is it possible to reconstruct the original square using just this information?

In the first pencil case, there is a lilac pen, a green pencil and a red eraser; in the second – a blue pen, a green pencil and a yellow eraser; in the third – a lilac pen, an orange pencil and a yellow eraser. The contents of these pencil cases are characterised by such a pattern: in every two of them exactly one pair of objects coincides in color and purpose. What should lie in the fourth pencil case, so that this pattern is preserved? $($In each pencil case, there are exactly three objects: a pen, a pencil and an eraser$)$.

Three friends – Peter, Ryan and Sarah – are university students, each studying a different subject from one of the following: mathematics, physics or chemistry. If Peter is the mathematician then Sarah isn’t the physicist. If Ryan isn’t the physicist then Peter is the mathematician. If Sarah isn’t the mathematician then Ryan is the chemist. Can you determine which subject each of the friends is studying?