**Problem: **Find the sum of all the even numbers in the Fibonacci sequence whose values do not exceed 4 million.

**Q: **What is the minimum section of the sequence that we need to keep in memory at any one time?**A: **3 elements – current element and previous two elements (which are used to calculate the current element).

**Q: **What is the starting point?**A: **1, 1, 2 (the first three elements).

**Q: **What is the rule to update the elements?**A: **Remove element 0, push elements 1 and 2 back one space, recalculate the new element 2 as the sum of elements 0 and 1.

**Memory requirements: **3 integers to hold the current element and the previous elements, and 1 integer for the sum of all even elements.

<?php declare(strict_types=1); error_reporting(E_ALL); define('MAX_SEQUENCE', 4000000); // Fibonnaci sequence actually starts 1, 2 but pretending it is 1, 1, 2 allows // us to use the same logic for every step instead of treating the first one // as a special case $sequence = [1, 1, 2]; $sum = 0; while ($sequence[2] <= MAX_SEQUENCE) { if ($sequence[2] % 2 === 0) { $sum += $sequence[2]; } // Move all elements back one space, then recalculate current element $sequence[0] = $sequence[1]; $sequence[1] = $sequence[2]; $sequence[2] = $sequence[0] + $sequence[1]; } print("$sum\n");