Puzzle 29 | (Car Wheel Puzzle)

Puzzle: A car has 4 tyres and 1 spare tyre. Each tyre can travel a maximum distance of 20000 miles before wearing off. What is the maximum distance the car can travel before you are forced to buy a new tyre? You are allowed to change tyres (using the spare tyre) an unlimited number of times. 

Answer: 25000 kms
Solution: Divide the lifetime of the spare tyre into 4 equal part i.e., 5000 and swap it at each completion of 5000 miles distance. 
Let four tyres be named as A, B, C and D and spare tyre be S.

• 5000 KMs: Replace A with S. Remaining distances (A, B, C, D, S) : 15000, 15000, 15000, 15000, 20000. 
  

• 10000 KMs: Put A back to its original position and replace B with S. Remaining distances (A, B, C, D, S) : 15000, 10000, 10000, 10000, 15000. 
  

• 15000 KMs: Put B back to its original position and replace C with S. Remaining distances (A, B, C, D, S) : 10000, 10000, 5000, 5000, 10000. 
  

• 20000 KMs: Put C back to its original position and replace D with S. Remaining distances (A, B, C, D, S) : 5000, 5000, 5000, 0, 5000. 
  

• 25000 KMs: Every tyre is now worn out completely. 
  

All tyres are used to their full strength. 

Related Amazon interview question

There are n pencils, each having l length. Each can write 4 kilometres. After writing 4 kilometers it has l/4 length. One can join 4 pencils which are having l/4 length and can make 1 pencil. One can’t make pencil of pieces if remaining pieces are 3 or 2 or 1 in number but one can include these remaining pieces whenever needed. 
Write a relation independent of l, length of the given pencil, for how much one can write from n pencils. 
Examples:

Input: 4
Output: 20

Recursive Approach: 
Suppose we use 3 pencils that will 12 and generate 3 used pencils, now if the remaining pencils are greater than zero at least 1 unused pencil can be used with those 3 unused to write 4 and that will generate 1 more unused pencil. This will keep repeating.

if(n-3 >= 1){
  f(n) = f(n-3) + 12 + 4
} 
else{
  // Used pencil that cannot be used
  f(n) = 4*n
}

Below is the implementation of the above approach:

C

int count(int n)
{
    if (n < 4) {
        return (n * 4);
    }
    else {
        return (16 + count(n - 3));
    }
}

Java

static int count(int n)
{
    if (n < 4) {
        return (n * 4);
    }
    else {
        return (16 + count(n - 3));
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Python3

def count( n):
    if (n < 4):
        return (n * 4)
    else:
        return (16 + count(n - 3))

# This code is contributed by Abhijeet Kumar(abhijeet19403)

C#

static int count(int n)
{
    if (n < 4) {
        return (n * 4);
    }
    else {
        return (16 + count(n - 3));
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Mathematical Approach O(1): 
Above relation can be optimized in O(1)

// x is max no of time we can 
//subtract 3 without n-3 <= 3
n - 3*x <= 3     
x  >  (n-3)/3
i.e. n/3 - 1 if it divides exactly
else n/3

Below is the implementation of the above approach: 

CPP

// C++ program to find relation independent of l
// length of the given pencil, for how much one
// can write from n pencils.

#include <bits/stdc++.h>
using namespace std;

// Function to find no of pencils
int count(int n)
{
    int x = (n / 3) - 1;
    if (n % 3) {
        x++;
    }
    return (4 * x + 4 * n);
}

// Driver function
int main()
{
    int n = 5;
    cout << count(n) << endl;
}

Java

// Java program to find relation independent of l
// length of the given pencil, for how much one
// can write from n pencils.
class GFG
{

// Function to find no of pencils
static int count(int n)
{
    int x = (n / 3) - 1;
    if (n % 3 > 0)
    {
        x++;
    }
    return (4 * x + 4 * n);
}

// Driver code
public static void main(String[] args)
{
    int n = 5;
    System.out.print(count(n) +"\n");
}
}

// This code is contributed by PrinciRaj1992

Python3

# Python3 program to find relation independent of l
# length of the given pencil, for how much one
# can write from n pencils.

# Function to find no of pencils
def count(n):
    x = (n // 3) - 1;
    if (n % 3 > 0):
        x+=1;

    return (4 * x + 4 * n);

# Driver code
if __name__ == '__main__':
    n = 5;
    print(count(n));

# This code is contributed by PrinciRaj1992

C#

// C# program to find relation independent of l
// length of the given pencil, for how much one
// can write from n pencils.
using System;

class GFG
{

// Function to find no of pencils
static int count(int n)
{
    int x = (n / 3) - 1;
    if (n % 3 > 0)
    {
        x++;
    }
    return (4 * x + 4 * n);
}

// Driver code
public static void Main(String[] args)
{
    int n = 5;
    Console.Write(count(n) +"\n");
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript program to find relation independent of l
// length of the given pencil, for how much one
// can write from n pencils.

// Function to find no of pencils
function count(n)
{
    let x = Math.floor(n / 3) - 1;
    if (n % 3 > 0)
    {
        x++;
    }
    return (4 * x + 4 * n);
}

// Driver code
let n = 5;
document.write(count(n) +"<br>");

// This code is contributed by rag2127
</script>

Output:

24