<p>A four-digit integer, WXYZ, in which W,X,Y,Z each represent a different digit, is formed according to the following rules:</p>
<li>X= W+Y+Z</li>
<li>W= Y+1</li>
<li>Z= W-5</li>
</ol>
<p>What is the four-digit integer?</p>
<p>I’m just going to rabble out my thought process you can read and (hopefully) understand where my answer comes from.</p>
<p>X has to be largest. That’s a given. X has to at least be 3.
W is the largest and has to be at least 5. </p>
<p>Let’s go ahead and make W=5, so Y=4, and, z=0. And that would make X=9.</p>
<p>… Works out. Wow, first try.</p>
<p>Piecing it together: WXYZ = 5940. :)</p>
<p>Ok, heres how you do it without guessing:</p>
<p>X is obviously the largest and Z is obviously the smallest, so you write X in terms of Z:</p>
<p>X=(Z+5)+(Z+4)+Z
X=3Z+9</p>
<p>Since X is a single digit integer, therefore the largest value it can be is a 9.
We can easily see that Z must be 0 and X must be 9.</p>
<p>Consequently, W=Z+5=5 and Y=Z+4=4
There the four-digit integer is 5940.</p>