# 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 each of the three was equal to the sum of the remaining two. The conductor said that it is not a problem, and tried to help the numbers. On the contrary, the dispatcher claimed that it was not possible. Decide who is right.

**Result****Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):**

**Showing 1 comment:**

**Dr Math**

Dispatcher is right. In each wagon shall be the sum of the numbers even. In one wagon must sit 9 and therefore the next two numbers whose sum is 9 and overall sum in the wagon is 18. The total sum of all numbers is 45 and the other two wagons already account for 45-18 = 27. However even number 27 can not be decomposed into the sum of two even numbers (in each wagon, the sum is always even). And so the task is not a solution and dispatcher's right.

9 months ago 1 Like

#### To solve this example are needed these knowledge from mathematics:

## Next similar examples:

- Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Game room

Winner can took win in three types of jettons with value 3, 30 and 100 dollars. What is minimal value of win payable in this values of jettons? - Plumber

Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it? - Diofant equation

In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Rectangles

How many rectangles with area 3002 cm^{2}whose sides is natural numbers are? - Amazing number

An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers. - Z9-I-4

Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi - Plums

In the bowl are plums. How many would be there if we can divide it equally among 10, 12 and 14 children? - Cherries

Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl? - Mr. Zucchini

Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and - 7 digit number

If 3c54d10 is divisible by 330, what is the sum of c and d? - Birthdate

Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend? - Divisibility

Is the number 146025 divisible by 6? - No. of divisors

How many different divisors has number ?? - Diofant 2

Is equation ? solvable on the set of integers Z? - Primes 2

Which prime numbers is number 2025 divisible? - Group

Group of kids wanted to ride. When the children were divided into groups of 3 children 1 remain. When divided into groups of 4 children 1 remain. When divided into groups of 6 children 1 missed. After divided to groups of 5 children its OK. How many are t