A small warehouse near Samarkand packs jars of apricot jam for a supermarket chain. This week a single order arrived: 252 jars, to be packed into identical cartons with none left over.
The warehouse has cartons in several sizes, but the supermarket set a rule: each carton must hold at least 10 jars and at most 20, because heavier cartons are hard to lift and lighter ones waste space on the truck.
Sardor, the shift supervisor, wrote the number 252 on a board and began to look for the sizes that divide it evenly. Two and three came first, since the number is even and its digits add up to nine. Seven followed, because seven times thirty-six is 252.
From there he listed the pairs: twelve cartons of twenty-one, fourteen of eighteen, eighteen of fourteen, twenty-one of twelve. Only three sizes fitted the supermarket's rule: 12, 14 and 18 jars per carton.
He chose 12. "Twelve is the size our customers already know," he said, "and it gives us exactly 21 cartons." A carton of 15 would have been easier to carry, but 252 jars would have left 12 jars over.
The order left on Friday, every carton full and none half empty.