Shahlo owns a small restaurant near the business district in Tashkent. Every weekday she serves a set lunch: one soup, one main course and one dessert. Her menu lists 4 soups, 5 main courses and 3 desserts.
Her nephew, who was studying for a business exam, told her that the restaurant already offered 60 different lunches, because each of the 4 soups can go with each of the 5 mains, and each of those 20 pairs can go with each of the 3 desserts. Shahlo liked the number. She wanted a new sign for the window that said more than 100 different lunches.
Adding dishes costs money, so she asked which single addition would help most. One more soup would give 5 times 5 times 3, which is 75. One more main course would give 4 times 6 times 3, which is 72. One more dessert would give 4 times 5 times 4, which is 80. None of them was enough.
She tried two additions. A new soup and a new dessert would give 5 times 5 times 4, exactly 100, which is not more than 100. Two new desserts would also give exactly 100. Finally, one new dish in every category would give 5 times 6 times 4, which is 120.
Shahlo chose that option. The new soup and dessert were cheap to make, and the new main course used ingredients she already bought. The advertisement went up the following Monday: "120 different lunches, one price."
Her nephew pointed out the lesson. In a product, adding one item to the smallest group gives the biggest jump: the third dessert raised the total by a third, while the sixth main course raised it by only a fifth.