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Post Archives from the ‘Puzzles’ Category



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 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
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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.

Antipodal points

Posted on: September 6th, 2015 by
2

Let f(t) be a continuous periodic function with period T, i.e.
  1. f(t) is continuous over reals.
  2. f(t+T) = f(t) for all real t.
Show that there always exists some time instant t_0 for which f(t_0) = f(t_0+T/2).

A dragon, a knight and poison fruits

Posted on: February 19th, 2015 by
2

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"

Space filling curve

Posted on: November 29th, 2014 by
1

Can you find a continuous function from the unit interval [0,1] to the unit square [0,1]^2? 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 400 coins, one can cover the entire surface area of Continue reading the story "Coin covering puzzle"

Parabola puzzle

Posted on: November 25th, 2014 by
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Let y=ax^2+b_1x+c_1 and y=ax^2+b_2x+c_2 be two parabolas with the same coefficient for the x^2 term. The y-intercepts of the two parabolas are (0,c_1) and (0,c_2) respectively. Let the two parabolas intersect at (x_1,y_1) and let the tangent to the two parabolas drawn at (0,c_1) and (0,c_2) intersect at (x_2,y_2). Show using physics that x_1=x_2. Hint: Assume x is time and y is space, and there is Continue reading the story "Parabola puzzle"

Find the product

Posted on: October 13th, 2014 by
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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 f(x) = \frac{x^2+x+1}{x^2+x+2}. Show that for real x, 3/7\le f(x) \le 1.

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 the BRICS nation. You may note that all 5 BRICS Continue reading the story "BRICS bank and Erlang's formula"

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