Go green, plant trees

Number Theory Level 4

In a school's $\color{#20A900}{\textbf{Go Green movement}}$ , they planned to take a tree-plantation event.

They have " $\color{#69047E}{k}$ " $\color{#20A900}{\text{plants}}$ for planting. The $\color{#D61F06}{\text{math teacher}}$ of the school tells that if they decide to plant them in ' $x$ ' rows, then ' $y$ ' $\color{#20A900}{\text{plants}}$ remain. The following table shows the values of $x$ and $y$ as seen by the teacher.

$\color{#3D99F6}{ \begin{array}{|c||c|} x & y \\ \hline 17&3\\ 19&4\\ 23&7\\ 29&12\\ \end{array} }$

Teacher asks the students to find the number of plants, i.e. $\color{#69047E}{k}$

Can you help the students by telling what is the $\color{#3D99F6}{\text{positive integer}}$ $\color{#69047E}{k}$ , if it is the smallest to satisfy the above property ?

Most probably, after you get the answer, you'll say "It's indeed a huge movement to 'Go green', so many plants ! "

The answer is 63464.

3 solutions

Aditya Raut
Aug 5, 2014

The number theory approach uses the repeated application of $\textbf{Chinese Remainder Theorem}$ and is similar to the solution i wrote here

But I just started learning programming by self study, so here is the python code that prints the number directly.

img

Hence the answer is $\boxed{63464}$

222222222 Trivial By Python, LOL

Dinesh Chavan - 6 years, 10 months ago

Yeah, too much, 3 much, 4 much..... trivial !

Aditya Raut - 6 years, 10 months ago

I've started to hate CRT after this!!!!!!!!!!!!!!!!! Aaaaaaaaaaaaaaaaaaaaarghhhhhhhhhhhhhh!!!!!!!!!!!

Krishna Ar - 6 years, 8 months ago

Was this movement taken up in your school ????? :-)

Parth Bhardwaj - 6 years, 3 months ago

cud anyone say wat is the way to solve the prob other than the comp. coding .....

Ganesh Ayyappan - 6 years, 5 months ago

Parth Bhardwaj
Feb 28, 2015

I also used the chinese remainder theorem.And got 63464.

Vaibhav Borale
Aug 5, 2014

I used Turbo C code simply!!!!!

Void main()

{ long int i;

int a,b,c,d;

a=3;b=4;c=7;d=12;

for(i=1;1<100000;i++)

{

      if(i%17==a)
        {if( i%19==b )
           {if( i%23==c )
              {if( i%29==d)

        { printf("Required number is %lu",i); }

                }
             }
          }

}

getch(); }

i too solved it the same way :D

void main()

{
    long i=0,k=0;
    do
    {
    i++;
    if(i%17==3 &  i%19==4 & i%23==7 &  i%29==12)
    k=i;
    }
    while(k==0);
    cout<<k; 
    }

Sagar Gupta - 6 years, 10 months ago

Go green, plant trees

The answer is 63464.

3 solutions

void main()

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