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 Show Problem 61
This gave me a headache. I was about to give up when I recalled that recursion is a very powerful tool and is very suitable for this question. The code does not look so pretty or concise but it is really powerful. I think you can figure out easily what I tried to [...]

Finally, I have found a very efficient answer for Problem 72. It runs under 1 seconds. It uses prime sieve of Eratosthenes.

Here is the code in Java

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import java.util.Arrays;
 
public class Problem72 {
 
public static void main(String args[])
{
int n=1000000;
int[] phi = new int[n+1];
for (int i=0; i<n+1; i++)
phi[i]=i;
 
boolean[] p = new boolean[n+1];
Arrays.fill(p, true);
p[0]=false;
p[1]=false;
for (int i=2; i<=n; i++)
{
 
if [...]

Show Problem 102
First of all we need a method to check whether a point is in the triangle or not. This site has some useful info regarding this issue. Actually, it is for three dimension but two dimensions is applicable if we set the third dimension to zero always. All we need to code is [...]

Show Problem 62

For this one I used a map. I calculated the cubes for integers till 10000. Then I sorted every cube. Using a hashmap I calculated the frequency of each sort. If the freq is 5, that gives us the combination. Using another hashmap I associated the integer before cube calculation with the combination. [...]

Show Problem 112

This one is very easy if you know the trick. Here is the trick. If you sort a number ascendingly and if it is still equals the same number then it is an increasing one. If you sort it descendingly and is still the same number it is a decreasing one. If neither [...]

This problem was fun. You have to come up with a way to count the rectangles in a rectangular grid. I used a four nested loop to count the rectangles. First two loops specify the grid size. Then the other two nested loops do the actual work. I assumed that the answer would be in [...]

When I first solved this problem I used BigIntegers. It took about 30 minutes to find the answer. The reason for that is I used BigIntegers and a binarysort in a loop. In fact the numbers used do not exceed integer limit so there is no need to use BigIntegers. So I present the more [...]

Hi everyone. It has been a while. In meantime I have discovered how fun it was to solve projecteuler.net problems. From now on I decided to publish my answers here. Actually, I was publishing them in the forum section of javaist. However, there has been some spamming there so I decided to carry my answers [...]