Ten bims and ten boms went to lunch and sat randomly at a large rotating table. Each bim ordered a nim and each bom ordered a nom. The waiter rushed the order, but in haste forgot who ordered what and placed the orders randomly. Bims and boms were not happy and promptly called the manager. The manager apologized and offered to resolve the issue by simply rotating the table. Is it true that the manager can always rotate the table so that at least half of the ordered dishes are placed correctly