Rectangular 2885
A total of ten exhibitors gathered at the long-haired cat show. It was exhibited in a rectangular room with two rows of tables as shown. The cats were marked with different numbers from 1 to 10, and one cat sat on each table. Determine which cat was rated the best at the show if you know that:
a) the sum of the numbers of cats sitting opposite each other was always the same,
b) the sum of the numbers of each two cats sitting next to each other was even,
(c) the product of the numbers of each of the two cats sitting next to each other in the lower row is a multiple of 8,
d) cat number 1 is not on edge and is further to the right than cat number 6,
e) the cat sitting in the lower right corner won.
a) the sum of the numbers of cats sitting opposite each other was always the same,
b) the sum of the numbers of each two cats sitting next to each other was even,
(c) the product of the numbers of each of the two cats sitting next to each other in the lower row is a multiple of 8,
d) cat number 1 is not on edge and is further to the right than cat number 6,
e) the cat sitting in the lower right corner won.
Correct answer:

You need to know the following knowledge to solve this word math problem:
Themes, topics:
Grade of the word problem:
Related math problems and questions:
- Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of the three was equal to the sum of the remaining two. The conductor said
- Decide
The rectangle is divided into seven fields. On each box is to write just one of the numbers 1, 2, and 3. Mirek argues that it can be done so that the sum of the two numbers written next to each other is always different. Zuzana (Susan) instead argues that
- Clubhouse
There were only chairs and tables in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs
- Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
- Three cats
If three cats eat three mice in three minutes, after which time 90 cats eat 90 mice?
- School group
There are five girls and seven boys in the group. They sit in a row next to each other. How many options if no two girls sit next to each other?
- Contestants
In the competition, it was possible to get 0-5 points. Five of the 15 best contestants have earned 5 points or 4 points (which have won 10 contestants). The number of contestants who scored 3 points was the same as those who did not get any points. Calcul
- Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer, there were six cubes (in one row) in six rows. In each subsequent layer, always one cube and one row less. What volume in cm³ did the whole tower have?
- Three-digit 9601
Majka researched multi-digit numbers, in which odd and even numbers alternate regularly. Those who start with an odd number are called comics, and those who start with an even number are called cheerful. (Eg, number 32387 is comic, and number 4529 is hila
- Twins with friend
The twins Danka and Janka went to the cinema with their friend Betka. Only six seats in the second row were available in the cinema. The twins want to sit next to each other. Danka is always to the right of Janka, and Betka is near one of them. How many m
- Equivalent expressions
A coach took his team out for pizza after their last game. There were 14 players, so they had to sit in smaller groups at different tables. Six players sat at one table and got four small pizzas to share equally. The other players sat at a different table
- Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of
- Remembers: 28341
My mother forgot the PIN code of her ATM card, which consisted of 4 different numbers. Help her put it together if she remembers: And - all the numbers were even B - zero in the pin code was not C - the first number was a multiple of the second number, wh
- Cinema
How many rows of seats are in the stands if you know that the first row has 24 seats and the last 50 seats, and each subsequent row has two more seats than the row before? How many seats are in the stands?
- Spartakiada
Practitioners lined up in rectangles with a row with four, five, or six exercisers, one always missing an entire rectangle. How many exercisers were on the field, if they have estimated not been more than 100?
- Lesson exercising
In the lesson on physical education, pupils are first divided into three groups so that each has the same number. They redistributed, but into six groups. And again, it was the same number of children in each group. Finally, they were divided into nine eq
- Velocity ratio
Determine the ratio at which the fluid velocity in different parts of the pipeline (one piece has a diameter of 5 cm and the other has a diameter of 3 cm) when you know that every point of the liquid is the product of the area of the tube [S] and the flui