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Invert 3 signals using 2 NOT gates

Posted on: February 9th, 2016 by
1

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 [Read the full story ...]

1988

Posted on: February 7th, 2016 by
Comments Requested

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.

Antipodal points

Posted on: September 6th, 2015 by
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Let be a continuous periodic function with period , i.e. is continuous over reals. for all real . Show that there always exists some time instant for which .

A dragon, a knight and poison fruits

Posted on: February 19th, 2015 by
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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 [Read the full story ...]

Space filling curve

Posted on: November 29th, 2014 by
1

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?

Coin covering puzzle

Posted on: November 27th, 2014 by
2

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 [Read the full story ...]

Parabola puzzle

Posted on: November 25th, 2014 by
Comments Requested

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, [Read the full story ...]

Find the product

Posted on: October 13th, 2014 by
2

What is (1-1/4)(1-1/9)(1-1/16)....(1-1/n^2)? - via Mind your decision

Range finder

Posted on: October 12th, 2014 by
3

Let . Show that for real , .

BRICS bank and Erlang's formula

Posted on: July 28th, 2014 by
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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 [Read the full story ...]


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