<PRE><B>Question 370999</B>
&lt;br&gt;&lt;font face=&quot;Tahoma&quot;&gt;Let x be the first even integer. &lt;br&gt;

Then the next three consecutive even integers are x+2, x+4, and x+6.&lt;br&gt;

Now we are given:&lt;br&gt;

{{{x+(x+2)+(x+4)+(x+6)=182}}}&lt;br&gt;

{{{4x+12=182}}}&lt;br&gt;

{{{4x=170}}}&lt;br&gt;

{{{x=42.5}}}&lt;br&gt;

Unfortunately, this proves that it is NOT possible to have 4 consecutive even integers that add up to 182, because 42.5 is NOT an even integer.&lt;br&gt;

This also proves that it is not possible to have 4 consecutive odd integers which add up to 182, because 42.5 is also not an odd integer!&lt;br&gt;

Perhaps your sum of 182 is wrong?&lt;br&gt;

The problem as written has no solution!&lt;br&gt;

However, if you change the sum to 172, then you would have 40, 42, 44, and 46 as the 4 consecutive integers which add up to 172.&lt;br&gt; 

Also, 42, 44, 46, and 48 add up to 180.&lt;br&gt;

In addition, 44, 46, 48, and 50 add up to 188.&lt;br&gt;

I hope this helps!&lt;br&gt;</PRE>