Without using any math terms at all:<p>Suppose you&#x27;ve got a list of numbers:<p><pre><code>    5, 11, 26, 13, 215, 55, 68, 99, 3, 7, 41
</code></pre>
And I ask: &quot;Do any of these numbers together add up to 126?<p>You might have to try every combination of numbers to get an answer. It can be very slow to do, trying every single combination (imagine a list with thousands of numbers, and a very long goal number). Maybe there are no combinations!<p>But once you have an answer:<p><pre><code>    11 + 13 + 99 + 3 = 126
</code></pre>
It is very easy to verify that the provided answer is correct (are all those numbers in my list? Yes, verified!)<p>Compare that problem to this one: Is this list of numbers in ascending order?<p><pre><code>    4, 7, 11, 22, 6, 35
</code></pre>
The answer is &quot;No, because of the 6.&quot; Finding the answer is much faster because you can do it on one read-through of the list. You aren&#x27;t checking a huge number of potential combinations or anything.<p>The first problem is in the class of problems called NP-Hard.<p>Oof. Getting lengthy so I&#x27;ll shush here. Hope that gives you an intuitive feel for it.