Few more challenges on ProjectEuler

ProjectEuler/027/problem27.php

@@ -0,0 +1,30 @@
+<?php
+function is_prime($prime) {  
+    if($prime < 1)
+    { 
+        return false;
+    }
+	if($prime == 1) 
+		return true;
+	if($prime == 2)
+		return true;
+    $sqrt = sqrt($prime);
+    for ($i = 3; $i <= $sqrt; $i+=2){
+        if ($prime%$i == 0) return false; 
+    } 
+    return true; 
+} 
+$high = 0;
+$max_primes = 0;
+for($a=-999; $a<1000; $a++) {
+	for($b=-999; $b<1000; $b=$b+2) {
+		$n=0;
+		while(is_prime($n*$n + $a * $n + $b)) {
+            $n++;
+                if($n > $max_primes) {
+                    $max_primes = $n;
+                    echo "max: $n a: $a b: $b\n";
+            }
+		}
+	}
+}

ProjectEuler/031/problem31.php

@@ -0,0 +1,34 @@
+<?php
+define("TOTAL", 200);
+$combo=0;
+$sum = 200;
+
+for ($a = 0; $a <= (TOTAL / 200); $a++) {
+    $sum_a = TOTAL - ($a * 200);
+    for ($b = 0; $b <= ($sum_a / 100); $b++) {
+        $sum_b = $sum_a - ($b * 100);
+        for ($c = 0; $c <= ($sum_b / 50); $c++) {
+            $sum_c = $sum_b - ($c * 50);
+            for ($d = 0; $d <= ($sum_c / 20); $d++) {
+                $sum_d = $sum_c - ($d * 20);
+                for ($e = 0; $e <= ($sum_d / 10); $e++) {
+                    $sum_e = $sum_d - ($e * 10);
+                    for ($f = 0; $f <= ($sum_e / 5); $f++) {
+                        $sum_f = $sum_e - ($f * 5);
+                        for ($g = 0; $g <= ($sum_e / 2); $g++) {
+                            $sum_g = $sum_f - ($g * 2);
+                            for ($h = 0; $h <= ($sum_g / 1); $h++) {
+
+                                if ($a * 200 + $b * 100 + $c * 50 + $d * 20 + $e * 10 + $f * 5 + $g * 2 + $h == TOTAL) {
+                                    $combo++;
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+echo $combo;

ProjectEuler/033/problem33.php

@@ -0,0 +1,24 @@
+<?php
+$sum = [];
+
+for($n = 10; $n <= 99; $n++)
+{
+    for($d=$n+1;$d <= 99; $d++)
+    {
+        foreach([1,2,3,4,5,6,7,8,9] as $digit) 
+        {
+            $ns = (int)str_replace($digit, '', $n);
+            $ds = (int)str_replace($digit, '', $d);
+
+            if($n != $ns && $d != $ds && $d != 0 && $ds != 0) 
+            {
+                if($n/$d == $ns/$ds)
+                {
+                    echo "$n/$d = $ns/$ds\n";
+                    $sum[] = $ns/$ds;
+                }
+            }
+        }
+    }
+}
+echo array_product($sum).PHP_EOL;

ProjectEuler/035/problem35.php

@@ -0,0 +1,61 @@
+<?php
+
+function is_prime($prime) {  
+    if($prime < 1)
+        return false;
+
+	if($prime == 1) 
+		return true;
+	if($prime == 2)
+		return true;
+    $sqrt = sqrt($prime);
+    for ($i = 3; $i <= $sqrt; $i+=2){
+        if ($prime%$i == 0) return false; 
+    } 
+    return true; 
+}
+
+if (($handle = fopen("primes1000000.txt", "r")) !== FALSE) {
+    while (($data = fgetcsv($handle, 1000, ",")) !== FALSE) {
+        if ($data[1] >= 1000000)
+            break;
+        //If there's an even digit (or a 5) we can instantly exclude it as when rotated it will not not be a prime.
+        if (
+            strpos((string) $data[1], "0") !== false ||
+            strpos((string) $data[1], "2") !== false ||
+            strpos((string) $data[1], "4") !== false ||
+            strpos((string) $data[1], "5") !== false ||
+            strpos((string) $data[1], "6") !== false ||
+            strpos((string) $data[1], "8") !== false
+        ) {
+
+            continue;
+        }
+        $primes[] = (int) $data[1];
+    }
+    fclose($handle);
+}
+echo "File read\n";
+
+$count = 1+1; //2 and 5 are primes but not included
+foreach($primes as $prime) 
+{
+        //echo "Now testing $prime\n";
+        $newprime = $prime;
+        for($rotate = 1; $rotate < strlen($prime); $rotate++)
+        {
+            $newprime = substr($newprime, -1, 1).substr($newprime, 0, -1);
+            //echo "New prime: $newprime\n";
+            if(!in_array($newprime, $primes))
+            {
+                continue 2;
+            }
+
+        }
+        $count++;
+        echo $prime.PHP_EOL;
+
+
+}
+
+echo "Total: $count\n";

ProjectEuler/045/problem45.php

@@ -0,0 +1,47 @@
+<?php
+/**
+ * Triangle   Tn = n*(n+1)/2
+ * Pentagonal Pn = n*(3n-1)/2
+ * Hexagonal  Hn = n*(2n-1)
+ * T(285) = P(165) = H(143) = 40755
+ * Find next
+ */
+
+function Tn($n)
+{
+    return $n*($n+1)/2;
+}
+
+function Pn($n)
+{
+    return $n*(3*$n-1)/2;
+}
+
+function Hn($n)
+{
+    return $n*(2*$n-1);
+}
+
+echo "Tn(285)=".Tn(285).PHP_EOL;
+echo "Pn(165)=".Pn(165).PHP_EOL;
+echo "Hn(143)=".Hn(143).PHP_EOL;
+
+
+for($t = 285; $t < 100000; $t++) 
+{
+    $triangle[$t] = Tn($t);
+}
+
+for($p = 165; $p < 100000; $p++) 
+{
+    $pentagonal[$p] = Pn($p);
+}
+
+for($h = 143; $h < 100000; $h++) 
+{
+    $hexagonal[$h] = Hn($h);
+}
+
+$result = array_intersect($triangle, $pentagonal, $hexagonal);
+
+print_r($result);

primes100.txt

@@ -0,0 +1,100 @@
+1, 2, 2
+2, 3, 1
+3, 5, 2
+4, 7, 2
+5, 11, 4
+6, 13, 2
+7, 17, 4
+8, 19, 2
+9, 23, 4
+10, 29, 6
+11, 31, 2
+12, 37, 6
+13, 41, 4
+14, 43, 2
+15, 47, 4
+16, 53, 6
+17, 59, 6
+18, 61, 2
+19, 67, 6
+20, 71, 4
+21, 73, 2
+22, 79, 6
+23, 83, 4
+24, 89, 6
+25, 97, 8
+26, 101, 4
+27, 103, 2
+28, 107, 4
+29, 109, 2
+30, 113, 4
+31, 127, 14
+32, 131, 4
+33, 137, 6
+34, 139, 2
+35, 149, 10
+36, 151, 2
+37, 157, 6
+38, 163, 6
+39, 167, 4
+40, 173, 6
+41, 179, 6
+42, 181, 2
+43, 191, 10
+44, 193, 2
+45, 197, 4
+46, 199, 2
+47, 211, 12
+48, 223, 12
+49, 227, 4
+50, 229, 2
+51, 233, 4
+52, 239, 6
+53, 241, 2
+54, 251, 10
+55, 257, 6
+56, 263, 6
+57, 269, 6
+58, 271, 2
+59, 277, 6
+60, 281, 4
+61, 283, 2
+62, 293, 10
+63, 307, 14
+64, 311, 4
+65, 313, 2
+66, 317, 4
+67, 331, 14
+68, 337, 6
+69, 347, 10
+70, 349, 2
+71, 353, 4
+72, 359, 6
+73, 367, 8
+74, 373, 6
+75, 379, 6
+76, 383, 4
+77, 389, 6
+78, 397, 8
+79, 401, 4
+80, 409, 8
+81, 419, 10
+82, 421, 2
+83, 431, 10
+84, 433, 2
+85, 439, 6
+86, 443, 4
+87, 449, 6
+88, 457, 8
+89, 461, 4
+90, 463, 2
+91, 467, 4
+92, 479, 12
+93, 487, 8
+94, 491, 4
+95, 499, 8
+96, 503, 4
+97, 509, 6
+98, 521, 12
+99, 523, 2
+100, 541, 18