Feruza works in the purchasing department of a hotel chain in Bukhara. She was asked to find the price of one box of printer paper from a new supplier, who sold paper and ink only in mixed orders.
The first report from the supplier said that an order of three boxes of paper and two cartridges of ink had cost 13 dollars. That was one equation with two unknown prices, so it could not give either price alone.
A second report arrived the next day, and her colleague was delighted. "Now we have two equations," he said, "so we can solve for both prices." The second report said that six boxes of paper and four cartridges had cost 26 dollars.
Feruza looked more carefully. Every number in the second report was exactly twice the first. It described the same proportion of paper to ink, at the same prices, simply doubled. It was not a second piece of information at all, only the first one written again, and two copies of one fact leave the prices just as unknown as before.
To find both prices, she needed a genuinely new fact, one that described a different mix. She telephoned the supplier and asked for the price of ink on its own. The answer was two dollars a cartridge. Now the first report was enough: two cartridges cost four dollars, so three boxes of paper cost nine dollars, and one box cost three.
Her colleague asked how she had spotted it so quickly. "When two statements look different," she said, "divide one by the other. If every number cancels to the same ratio, they are the same statement in different clothes."