## 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
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
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
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 $f(x) = \frac{x^2+x+1}{x^2+x+2}$. Show that for real $x$, $3/7\le f(x) \le 1$.

## BRICS bank and Erlang's formula

Posted on: July 28th, 2014 by
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"