21:["$","span",null,{"className":"flex items-center gap-1 whitespace-nowrap min-w-0","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","stroke":"currentColor","strokeWidth":2,"strokeLinecap":"round","strokeLinejoin":"round","className":"lucide lucide-chevron-right h-3 w-3 shrink-0","children":[["$","path","mthhwq",{"d":"m9 18 6-6-6-6"}],"$undefined"]}],["$","span",null,{"className":"text-foreground font-medium truncate max-w-[150px] sm:max-w-[200px] md:max-w-[250px] lg:max-w-[300px]","title":"a,b -> |a-b| , starting with 1-2012 in a blackboard","children":"a,b -> |a-b| , starting with 1-2012 in a blackboard"}]]}] 24:T50b,The numbers

1, 2, ..., 2012

are written on a blackboard, in some order, each of them exactly once. Between every two neighboring numbers the absolute value of their difference is written and the original numbers are deleted. This process is repeated until only a number remains on the board. What is the largest number that can stay on the board?

Problem Statement