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

x = (Correct answer is: V)

Solution:

Try another example

Leave us a comment of this math problem 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.

1 year ago  1 Like Like

Next similar math problems:

1. Last digit
   What is the last number of 2016 power of 2017
2. Unknown number
   Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
3. Toy cars
   Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
4. 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.
5. Three numbers
   How much we increases the sum of three numbers when the first enlarge by 14, second by 15 and third by 16? Choose any three two-digit numbers and prove results.
6. Six-digit primes
   Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
7. Primes 2
   Which prime numbers is number 2025 divisible?
8. MO C–I–1 2018
   An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
9. Divisors
   The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
10. Divisibility 2
    How many divisors has integer number 13?
11. Sum of two primes
    Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
12. Find the sum
    Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
13. Pet store
    In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th
14. Bus 2
    On the 6-th stop 44 passengers take off from bus. Overall, the 6-th stop 13 passengers were added. How many passengers take on 6-th stop?
15. Multiples
    What is the sum of the multiples of number 7 that are greater than 30 but less than 56?
16. Tunnels
    Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any
17. Family
    The parents had 7 daughters. Each of them had one brother. How many members family had?