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"
Post Archives from the ‘Puzzles’ Category
Consider the inequality where 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.
Let be a continuous periodic function with period , i.e.
- is continuous over reals.
- for all real .
A knight and a dragon were dueling on a remote island. After a long time, they were tired of battle and decided to instead fight with their wits. The island consists of 7 different kinds of poison fruits, namely type 1, type 2, ... type 7. These fruits are magical and they work in a special way. If you eat a fruit of type i, … Continue reading the story "A dragon, a knight and poison fruits"
Can you find a continuous function from the unit interval to the unit square ? In other words, can you find a curve that passes through all points in a unit square?
100 identical circular coins are placed in a rectangular table such that no extra coin can be placed without overlapping with one of the coins already on the table. For the purpose of this puzzle, assume a coin is placed on a table as long as it's center lies on the table. Show that with 400 coins, one can cover the entire surface area of … Continue reading the story "Coin covering puzzle"
Let and be two parabolas with the same coefficient for the term. The y-intercepts of the two parabolas are and respectively. Let the two parabolas intersect at and let the tangent to the two parabolas drawn at and intersect at . Show using physics that . Hint: Assume x is time and y is space, and there is … Continue reading the story "Parabola puzzle"
Let . Show that for real , .
If you have been following news, you will know that the 5 BRICS nations, namely Brazil, Russia, India, Chian and South Africa, came together to form the BRICS bank. Each country contributed $10 billion to net $50 billion of initial capital. The purpose of the BRICS bank is to provide loans for infrastructure projects in the BRICS nation. You may note that all 5 BRICS … Continue reading the story "BRICS bank and Erlang's formula"