2015 Countdown Problem #10: A Very Very Long Number

Computer Science Level 3

A person writes the numbers 1 to 2015 together as $123456789101112131415…201320142015$ Calculate the total number of occurrences where ‘15’ appears in the whole number.

The answer is 152.

5 solutions

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Brock Brown
Dec 24, 2014

Done with four lines of Python:

s = ""
for i in xrange(1,2016):
    s = s + str(i)
print s.count('15')

Nikola Djuric
Dec 6, 2014

Numbers ending with 15 : 015,115,215,...,2015 (21 of them) but 1515 counted just once for now Numbers begining with 15:150-159,1500-1599, (110 of them) now 1515 counted second time Numbers between:1150-1159(10 of them) two numbers together 501|502,511|512...591|592 and 51|52(11 of them) So,there is 21+110+10+11=152 appears of '15'

Nice solution! :)

Wee Xian Bin - 6 years, 6 months ago

it is true

Ramanuj Jhawar - 6 years, 6 months ago

Wee Xian Bin
Dec 12, 2014

Here's the list of all the occurrences (not the solution) (spoiler alert):

1 to 100: 2 occurrences (123…141516…495051525354…)

101 to 200: 11 occurrences (115…150151152…158159…)

201 to 300: 1 occurrence (215)

301 to 400: 1 occurrence (315)

401 to 500: 1 occurrence (415)

501 to 600: 11 occurrences (501502…511512…515…521522…531532…541542…551552…561562…

571572…581582…591592…)

601 to 700: 1 occurrence (615)

701 to 800: 1 occurrence (715)

601 to 900: 1 occurrence (815)

901 to 1000: 1 occurrence (915)

1001 to 1100: 1 occurrence (1015)

1101 to 1200: 11 occurrences (1115…114911501151115211531154115511561157115811591160…)

1201 to 1300: 1 occurrence (1215)

1301 to 1400: 1 occurrence (1315)

1401 to 1500: 2 occurrences (1415…1500)

1501 to 1600: 100 occurrences (150015011502…15511552…15581559…15981599)

1601 to 1700: 1 occurrence: (1615)

1701 to 1800: 1 occurrence: (1715)

1801 to 1900: 1 occurrence: (1815)

1901 to 2000: 1 occurrence: (1915)

2001 to 2015: 1 occurrence: (2015)

public class Fifteen {

public static void main(String args[])
{
    char [] c = null; int fifteen_count=0; 
    StringBuilder s = new StringBuilder();
    for(int i=1;i<=2015;i++)
    {
        s.append(i);
        c= s.toString().toCharArray();

    }

    for(int j =0;j<c.length;j++)
    {

            if(c[j]=='5')
            {
                if(c[j-1]=='1')
                fifteen_count++;
            }


    }
    System.out.println(fifteen_count);
}

}

Ziad Skaik - 6 years, 6 months ago

Ok just to admit, I wrote a C++ program to double check my answer before I posted this problem :)

Wee Xian Bin - 6 years, 6 months ago

You mean to say that you did similar to what I did?

Ziad Skaik - 6 years, 6 months ago

@Ziad Skaik – Just to confirm I had the correct answer before posting this :)

Wee Xian Bin - 6 years, 6 months ago

Vatsalya Tandon
Dec 13, 2014

Three steps and you get the answer-

Create a computer program to print all numbers from 1 to 2015

I created a JAVA program-

public class Brilliant

{

void main()

{

    for(int i = 1 ; i<=2015; i++)

    {

        System.out.print(i);

    }

}

}

Compile and Copy the Output.
Paste the out put in "Notepad". Press Ctrl+F.

The number of times 15 comes is 152

And yes, Enjoy!

I enjoy the creative use of ctrl+f in this solution.

Brock Brown - 6 years, 5 months ago

Anna Anant
Dec 16, 2014

a = num2str([1:2015]); a(a==' ')=[]; s = 0;

for i = 1:length(a)-1 if [a(i) a(i+1)] == '15' s = s +1; i = i+1; end end s s = 152 Problem ??

2015 Countdown Problem #10: A Very Very Long Number

The answer is 152.

5 solutions

Discussions for this problem are now closed

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