<p>Given the function:</p>
<p>f(x) = f(398 - x) = f(2158 - x) = f(3214 - x) </p>
<p>what is the largest number of different values that could appear in the list f(0), f(1), f(2), ..., f(999)?</p>
<p>A.) 46
B.) 177
C.) 352
D.) 398
E.) 801</p>
<p>Explanations would be appreciated :}</p>
<p>I believe it is B.) 177? I had to do a bit of reading for this one. Turns out I didn’t know how to solve this one.
This may help you: [Euclidean</a> algorithm - AoPSWiki<a href=“you%20may%20want%20to%20see%20the%20second%20link%20first”>/url</a></p>
<p>I just wanted to say that I don’t think these are math level 2 problems. They wouldn’t be so hard, in my opinion. I did some online searching and confirmed that these problems are AIME problems. Kudos to your tutor for challenging you! The solution is also online most of the times so you can usually google search for it. See this: [url=<a href=“http://www.artofproblemsolving.com/Wiki/index.php/2000_AIME_I_Problems/Problem_12]2000”>Art of Problem Solving]2000</a> AIME I Problems/Problem 12 - AoPSWiki](<a href=“http://www.artofproblemsolving.com/Wiki/index.php/Euclidean_algorithm]Euclidean”>Art of Problem Solving)</p>
<p>these is no way that this is a math 2 problem</p>
<p>Could it be E.) 801?</p>
<p>The arguments of each of the four parts of the equation have ranges of 0 to 999, 398 to -601, 2158 to 1159, and 3214 to 2215, respectively as x takes on integral values from 0 to 999. I ignored the last two parts of the equation because their arguments did not intersect any of the others. So, f(x)=f(398-x) takes on 200 unique values on the interval [0, 199]. There are no new values for f(x) on the interval [200, 398] because 200=398-198, which was the argument for the second part of the equation when x was 198. However, f(x) takes on 601 new values on [399, 999]; we haven’t had 399 or -1 as arguments yet, etc. So, 200+601=801. I hope that that helped.</p>