Five of the six numbers 23, 41, 17, 35, $x$ and 29 are known. The range of the six numbers is 38, and $x$ is the largest of them. Find $x$.

Since $x$ is the largest, the smallest of the six is still 17, the smallest of the known values. Range = largest − smallest, so $x-17=38$ and $x=55$. Adding the range to the largest KNOWN value gives 41 + 38 = 79, which measures from the wrong end; subtracting it from 41 gives 3, a number that would not be the largest at all and would itself change the range to 38 by accident of being the smallest; and 38 is the range copied straight out of the question.