More progress

solutions/ProjectEuler/046/solve.php

@@ -0,0 +1,61 @@
+<?php
+/*
+It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+
+9  = 7  + 2 * 1^2
+15 = 7  + 2 * 2^2
+21 = 3  + 2 * 3^2
+25 = 7  + 2 * 3^2
+27 = 19 + 2 * 2^2
+33 = 31 + 2 * 1^2
+ 
+It turns out that the conjecture was false.
+
+What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
+*/
+
+$primes = [2];
+$composites = [];
+$twicesquares = [];
+
+function is_prime(int $n) :bool{for($i=$n**.5|1;$i&&$n%$i--;);return!$i&&$n>1;}
+
+for ($i= 3; $i<6000; $i += 2) {
+    if (is_prime($i))
+    {
+        $primes[] = $i;
+    }
+    else
+    {
+        $composites[] = $i;
+    }
+}
+
+for($i=1; $i<100; $i++)
+{
+    $twicesquares[] = 2*($i*$i);
+}
+
+foreach($composites as $composite)
+{
+    $count = 0;
+    foreach($primes as $prime)
+    {
+        if($prime > $composite)
+        {
+            break;
+        }
+        if(in_array($composite-$prime, $twicesquares))
+        {
+            $count++;
+            break;
+        }
+    }
+
+    if($count == 0)
+    {
+        echo "Found $composite\n";
+        die;
+    }
+}
+

solutions/ProjectEuler/047/solve.php

@@ -0,0 +1,16 @@
+<?php
+/*
+The first two consecutive numbers to have two distinct prime factors are:
+14 = 2 * 7
+15 = 3 * 5
+
+
+The first three consecutive numbers to have three distinct prime factors are:
+
+644 = 2^2 * 7 * 23
+645 = 3 * 5 * 43
+646 = 2 * 17 * 19
+
+Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
+*/
+

solutions/other/fibonacci.php

@@ -0,0 +1,18 @@
+<?php
+
+function fibonacci($n) {
+    if ($n <= 1)
+        return $n;
+    return fibonacci($n - 1) + fibonacci($n - 2);
+} 
+
+echo fibonacci(1).PHP_EOL;
+echo fibonacci(2).PHP_EOL;
+echo fibonacci(3).PHP_EOL;
+echo fibonacci(4).PHP_EOL;
+echo fibonacci(5).PHP_EOL;
+echo fibonacci(6).PHP_EOL;
+echo fibonacci(7).PHP_EOL;
+echo fibonacci(8).PHP_EOL;
+
+//1 1 2 3 5 8 13 21 34

solutions/other/multipleof3and5.php

@@ -0,0 +1,9 @@
+<?php
+//Write a program or solve manually to find the smallest positive number that is evenly divisible by all of the numbers from 1 to 20.
+$m3 = range(3, 1000, 3);
+$m5 = range(5, 1000, 5);
+
+$all = array_unique(array_merge($m3,$m5));
+
+echo array_sum($all);
+

solutions/other/numbergame.php

@@ -0,0 +1,26 @@
+<?php
+//$argv = ['', 556, 25, 75, 9, 4, 2, 9]; 
+//$argv = ['', 134, 100, 6, 1, 1, 6, 6 ];
+//$argv = ['', 306, 50, 1, 5, 1, 8, 7];
+$sum = (int)$argv[1]; 
+$input_numbers = array_slice($argv, 2);
+$operation = ['+','-','*','/'];
+
+$best_diff = $sum;
+while($best_diff != 0) {
+    shuffle($input_numbers);
+    $numbers = array_slice($input_numbers, random_int(1, sizeof($input_numbers)));
+
+    $exp = "";
+    foreach($numbers as $n){
+        $exp .= $n;
+        $exp .= $operation[random_int(0,3)];
+    }
+    $exp = substr($exp, 0, -1);
+    $s = eval("return $exp;");
+
+    if(abs($sum - $s) < $best_diff) {
+        $best_diff = abs($sum - $s);
+        echo "Found: $best_diff =\t$exp\n";
+    }
+}

solutions/other/primesum.php

@@ -0,0 +1,21 @@
+<?php
+
+function primeCheck($number){
+    if ($number == 1)
+    return 0;
+    for ($i = 2; $i <= $number/2; $i++){
+        if ($number % $i == 0)
+            return 0;
+    }
+    return 1;
+}
+
+$sum = 0;
+for($i=2; $i<=1000; $i++)
+{
+    if(primeCheck($i)) {
+        $sum += $i;
+    }
+}
+
+echo "Sum: $sum\n";

solutions/other/reversemultiple9.php

@@ -0,0 +1,27 @@
+<?php
+//Find a three-digit number such that when the digits are reversed and subtracted from the original number, the result is a multiple of 9.
+function numreverse($number) {
+
+    $numberStr = (string)$number;
+    $numberStr = strrev($numberStr);
+    return (int)$numberStr;
+}
+$i = 100;
+$good = 0;
+$bad = 0;
+while($i <=999) {
+    $num = $i - numreverse($i);
+
+    if($num != 0 && $num % 9 == 0) {
+        echo("\nFound $i");
+        $good++;
+    } else {
+        echo("\nNo $i");
+        $bad++;
+    }
+
+
+    $i++;
+}
+
+echo "\nGood: $good Bad: $bad";

solutions/other/sum44.php

@@ -0,0 +1,24 @@
+<?php
+//12857 multiplied by 7 gives 90099, and the sum of the digits of 90099 is indeed 27, not 44. Keep trying!
+
+function sumDigits($number) {
+    $sum = 0;
+    // converting number to string to access digits easily
+    $numberStr = (string)$number;
+    for ($i = 0; $i < strlen($numberStr); $i++) {
+        $digit = (int)$numberStr[$i];
+        $sum += $digit;
+    }
+    return $sum;
+}
+$i = 0;
+while(true) {
+    $i++;
+
+    $var = $i*7;
+
+    if(sumDigits($var) == 44) 
+    {
+        die("Found $i");
+    }
+}

solutions/other/sumdiv20.php

@@ -0,0 +1,21 @@
+<?php
+//Write a function to find the smallest number that is divisible by each of the numbers from 1 to 20.
+
+function sumdiv20() {
+    $i = 20;
+    while(true) {
+        $i += 20;
+
+        if($i %19== 0) {
+        if($i %18== 0) {
+        if($i %17== 0) {
+        if($i %16== 0) {
+        if($i %15== 0) {
+        if($i %14== 0) {
+        if($i %13== 0) {
+        if($i %12== 0) {
+        if($i %11== 0) {
+            return $i;
+        }}}}}}}}}
+    }
+}