Invert 3 signals using 2 NOT gates

Posted on: February 9th, 2016 by
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You have 3 boolean inputs A, B and C. You want to obtain NOT(A), NOT(B) and NOT(C) all at once. However you are allowed to use at most 2 NOT gates. You may use as many AND and OR gates as you like. You may not use any other gates. Can you build a circuit to achieve this? - Via multiple sources including a bonus homework Continue reading the story "Invert 3 signals using 2 NOT gates"

1988

Posted on: February 7th, 2016 by
Consider the inequality $\frac{1}{x-1} + \frac{2}{x-2} + \frac{3}{x-3} + \dots \frac{70}{x-70} \geq \frac{5}{4},$ where $x$ is real. Show that the sum of the lengths of the disjoint intervals that satisfy the above inequality is 1988. - via International Math Olympiad 1988.