By six

From the digits 1,2,3,4 we create the long integer number 123412341234. .. .. , which will have 962 digits. Is this number divisible by 6?

Correct result:

x =  1

Solution:

n=962 n1=n/4=962/4=4812=240.5 n2=⌊n1⌋=⌊240.5⌋=240 n3=n−4⋅ n2=962−4⋅ 240=2  s=n2⋅ (1+2+3+4)+1+2=240⋅ (1+2+3+4)+1+2=2403 s3=s/3=2403/3=801  12341234...123412 x=1n=962 \ \\ n_{1}=n/4=962/4=\dfrac{ 481 }{ 2 }=240.5 \ \\ n_{2}=\lfloor n_{1} \rfloor=\lfloor 240.5 \rfloor=240 \ \\ n_{3}=n-4 \cdot \ n_{2}=962-4 \cdot \ 240=2 \ \\ \ \\ s=n_{2} \cdot \ (1+2+3+4) + 1 + 2=240 \cdot \ (1+2+3+4) + 1 + 2=2403 \ \\ s_{3}=s/3=2403/3=801 \ \\ \ \\ 1234 1234 ... 1234 12 \ \\ x=1

Try another example


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!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Buildings
    prg The school stands 110 m from the church, which is 100 m beyond the town hall. Which building are closer to the church and how many times?
  • Sum of the digits
    numbers2 How many are two-digit natural numbers that have the sum of the digits 9?
  • 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.
  • Street numbers
    street Lada came to aunt. On the way he noticed that the houses on the left side of the street have odd numbers on the right side and even numbers. The street where he lives aunt, there are 5 houses with an even number, which contains at least one digit number 6
  • Log
    5962705_ad Worker cut his thick log to 6 pieces for 30 min. How long he cut log to 12 pieces?
  • Divisibility 2
    divisors How many divisors has integer number 13?
  • Math test
    numbers_1 In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?
  • Divisibility
    nice_circles Determine all divisors of number 84.
  • Number
    prime What number should be placed instead of the asterisk in number 702*8 to get a number divisible by 6?
  • Perpetrator
    snehulaci The perpetrator is a number that is smaller than the number 80. It is a multiple of five and it is odd. If we added up the tens and ones of this number we get number 8.
  • Janka and Danka
    books_3 Janka and Danka began to read the same day the books. Janka had 276 pages, Danka 204 pages. They agreed that both read every day the same number of pages until theirs books read. A) How many maximum pages they had to read the day to honor their agreement
  • Last page
    books_44 Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
  • Write decimals
    numbers_34 Write in the decimal system the short and advanced form of these numbers: a) four thousand seventy-nine b) five hundred and one thousand six hundred and ten c) nine million twenty-six
  • Exhibition
    skola_vola The teacher paid for 280 Kč for 4.A students for admission to the exhibition. How many students were on the exhibition?
  • Hens and pigs
    pigs_2 Hens and pigs have 46 feet in total. At least how much can heads have?
  • Prime factors
    prime Write 98 as product of prime factors
  • Symbols
    my If 2*3 = 60 ; 3*4 = 120 and 4*5 = 200, what is 2*5?