Modulo

All you asked for was a quiet night of mind-numbing puzzle solving. Just a few simple math problems to ease your mind into the shallows of slumber. But this cursed puzzle keeps giving you numbers for blocks you haven't solved yet. And your friend's score keeps climbing, while yours has stumbled backwards thanks to that wayward misplaced digit from a minute ago. Why did you agree to a base-16 challenge? You're an upstanding model citizen, a firm believer in the banality of decimals. Hexadecimals are for hackers and wizards, and you wonder how strange it is to wish for an extra three fingers to sprout on each hand. Suddenly, you see it. You scan up and down, and realize a thin sliver of empty blocks snaking up the puzzle leaves an opening for your glorious comeback. A momentary rush jolts your brain as you hover over the lonely block hanging perilously from the very end...