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) Wrong answer

Solution:

a=1+2+3+4+5+6+7+8+9=45 s1=9+9=18 s2=a+a=45+45=90 s3=b+b t=as1=4518=27 27=s2+s3 27=2a+2b 27/2=a+b x=Va=1+2+3+4+5+6+7+8+9=45 \ \\ s_{1}=9 + 9=18 \ \\ s_{2}=a + a=45 + 45=90 \ \\ s_{3}=b + b \ \\ t=a - s_{1}=45 - 18=27 \ \\ 27=s_{2} + s_{3} \ \\ 27=2a + 2b \ \\ 27/2=a+b \ \\ x=V



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

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.

2 years ago  1 Like
avatar









Next similar math problems:

  • Unknown number
    unknown 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 prod
  • Amazing number
    numbers4 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.
  • Four-digit numbers
    numberline Find four-digit numbers where all the digits are different. For numbers, the sum of the third and fourth digits is twice the sum of the first two digits, and the sum of the first and fourth digits is equal to the sum of the second and third digits. The di
  • Primes 2
    prime_table Which prime numbers is number 2025 divisible?
  • MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  • Multiples
    sedma_1 What is the sum of the multiples of number 7 that are greater than 30 but less than 56?
  • Digit sum
    numbers_41 Determine for how many integers greater than 900 and less than 1,001 has digit sum digit of the digit sum number 1.
  • Sum of two primes
    prime_1 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.
  • Quiz or test
    test_2 I have a quiz with 20 questions. Each question has 4 multiple choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to #1 = C, then it will always be equal
  • Toy cars
    numbers2_13 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?
  • Three numbers
    dice 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.
  • Pet store
    fish 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 tha
  • Six-digit primes
    numberline_1 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?
  • One hundred stamps
    stamp_4 A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
  • Bus 2
    bus2 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?
  • Family
    bigfamily A man and a woman have 6 daughters together (or - "with each-other" so that step-children are excluded). Each daughter has one brother. How many members are in the immediate family?
  • Tunnels
    Mysky 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