IOM 2016, Блиц — Задача 73

Olympiad of Metropolises, Moscow. Blitz Contest, September, 5 · 5 септември 2016 г.

Условие

How many different sets of values of boolean variables x1x_1, x2x_2, x3x_3, x4x_4, x5x_5, x6x_6, x7x_7, x8x_8, x9x_9, x10x_{10}, x11x_{11}, x12x_{12} satisfy all of the following conditions? The sign ¯ means NOT operation, sign & means AND operation, sign ∨\vee means OR and 0 means False.

{x1=x2‾ & (x1&x3‾∨x1‾&x3)=0x2=x3‾ & (x2&x4‾∨x2‾&x4)=0…x10=x11‾ & (x10&x12‾∨x10‾&x12)=0\begin{cases} \overline{x_1 = x_2}\,\&\,(x_1\&\overline{x_3} \vee \overline{x_1}\&x_3) = 0 \\ \overline{x_2 = x_3}\,\&\,(x_2\&\overline{x_4} \vee \overline{x_2}\&x_4) = 0 \\ \ldots \\ \overline{x_{10} = x_{11}}\,\&\,(x_{10}\&\overline{x_{12}} \vee \overline{x_{10}}\&x_{12}) = 0 \end{cases}

Решение

Внимание: Непълно решение

В архива няма официално решение на тази задача.

Оригинал в Архива: blitz.pdf