jump to navigation

## Problem of the Day #183: H.E.R.P. D.E.R.P.September 18, 2011

Posted by Seungln in : potd , add a comment

The robots H.E.R.P. and D.E.R.P. (don’t ask me what the acronyms stand for, because I don’t know either) are in love with each other, but they are $100$ feet away from each other. H.E.R.P. and D.E.R.P. decide to meet each other, and they give each other directions. They send out signals of their location every foot, and expect to arrive within $50$ iterations. However, due to the radio wave noise in their environment, there is a probability of $\displaystyle \frac{2}{7}$ that the signal will be incorrectly interpreted, in which case the two robots will turn $90^{\circ}$ either to the left or to the right, with equal probability. What is the expected value of iterations necessary for H.E.R.P. and D.E.R.P. will meet each other?

## Problem of the Day #182: U Can’t Touch This!September 17, 2011

Posted by Seungln in : potd , add a comment

Sreenath finds himself hovering in an amorphous prison cell. He tries to touch a wall and finds that he cannot get within $1$ meter of the surface that surrounds him. If Sreenath knows that this prison cell has a constant volume of $450$ meters cubed, then what is the maximum volume that Sreenath can occupy?

## Problem of the Day #179: Twins!September 14, 2011

Posted by Seungln in : potd , add a comment

Tandrew Ao has finally found his long-lost twin, Andrew Tao.

Andrew Tao is giving Tandrew Ao some math problems to work on. However, Tandrew Ao’s world has a math that is slightly different from the math of Andrew Tao’s world.

For example, when given the same equation: $7x^2 = -28$, Andrew Tao will say $\pm 2i$ as the answer. Tandrew Ao will say $\pm 2$ as his answer. Both are correct, depending on which math they use.

For another example, Andrew Tao will solve $4x^2 + 4x + 1 = 0$ as $x = \displaystyle -\frac{1}{2}$, while Tandrew Ao will solve it as $x = \displaystyle \frac{i}{2}$.

If so, then What would be Tandrew Ao’s solution for the equation $x^3 – 7x^2 + 14x – 8 = 0$ be?

## Problem of the Day #178: Twins!September 13, 2011

Posted by Seungln in : potd , add a comment

Andrew Tao has finally found his long-lost twin, Tandrew Ao.