21:["$","div",null,{"data-slot":"card","className":"bg-card text-card-foreground flex flex-col gap-6 rounded-xl border py-6 shadow-sm w-full max-w-4xl mx-auto hover:shadow-lg hover:border-primary/50 transition-all duration-200 cursor-pointer","children":[["$","div",null,{"data-slot":"card-header","className":"@container/card-header grid auto-rows-min grid-rows-[auto_auto] items-start gap-2 px-6 has-data-[slot=card-action]:grid-cols-[1fr_auto] [.border-b]:pb-6","children":["$","div",null,{"className":"flex justify-between items-start gap-4","children":[["$","div",null,{"className":"space-y-1","children":[["$","div",null,{"data-slot":"card-title","className":"text-xl font-bold hover:text-primary transition-colors","children":"domino tiling 9x9 board without two corners and center (VTRMC 2004 P4)"}],["$","p",null,{"className":"text-sm text-muted-foreground","children":["Source: ",""]}]]}],["$","div",null,{"className":"text-xs text-muted-foreground whitespace-nowrap","children":"8/2/2021"}]]}]}],["$","div",null,{"data-slot":"card-content","className":"px-6 space-y-4","children":["$","div",null,{"className":"prose dark:prose-invert max-w-none","children":["$","div",null,{"className":"latex","children":["$","span",null,{"className":"__Latex__","dangerouslySetInnerHTML":{"__html":"A

9\\times9

chess board has two squares from opposite corners and its central square removed. Is it possible to cover the remaining squares using dominoes, where each domino covers two adjacent squares? Justify your answer."}}]}]}]}],["$","div",null,{"data-slot":"card-footer","className":"items-center px-6 [.border-t]:pt-6 flex flex-wrap gap-2","children":[["$","span","combinatorics",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"combinatorics"}],["$","span","Tiling",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"Tiling"}]]}]]}]

Problem 4

Problems(1)