Bill-Splitting Nemeses

The two of you have been friends since college, but that hasn't stopped your competitive nature from butting heads at every turn, especially when it comes to splitting the cost of outings. Known among your social circle for being a penny-pincher, your meticulous calculations on splitting bills has caused more than one argument between you. This fateful day, an argument over the exact cost of a shared meal escalated, and the next thing you knew, you woke up together in a peculiar room, a note on the door reading: 'End this feud or the door stays locked.'