What a cool idea, I loved solving this one! I’m not really sure what the “I can eliminate contradictions” hint refers to, but the math hint was very helpful :)
Thank you! That hint is only helpful for one possible way someone could arrive at the solution. rot13: Ryvzvangvat pbagenqvpgbel fgngrzragf nyybjf lbh gb svyy va fbzr oynaxf jvgubhg haqrefgnaqvat gur ehyr. Ohg V svaq gung zber crbcyr guna V rkcrpgrq haqrefgbbq gur ehyr orsber gurl arrqrq gb qb gung.