На дне рождения у Дядьки Черномора присутствовали все 33 богатыря. Черномор угощал их тортом по очереди. Первый богатырь съел 1/16 всего торта, второй - 1/17 оставшегося, третий 1/18 оставшегося и так далее. Наконец 33-й богатырь съел 1/48 оставшегося куска, и то, что осталось, съел Черномор. Кто съел больше: первый богатырь или Черномор? Во сколько раз? Если богатырь и Черномор съели поровну, в ответ запишите 1.

Давайте посчитаем, сколько торта съел каждый богатырь:

1-й богатырь: 1/16 2-й богатырь: 1/17 * (1 - 1/16) = 1/17 * 15/16 3-й богатырь: 1/18 * (1 - 1/16 - 1/17 * 15/16) = 1/18 * 16/17 * 15/16 ... 33-й богатырь: 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... - 1/31 * ...) = 1/48 * (1 - 1/16 - 1/17 * 15/16 - ... -