thnik again!

From yesterday’s mail:

“It makes me extremely angry that the problems in this blog are so difficult that only people with a pdf can solve them!”

Therefore, here is an easy problem everyone can solve:

“In a room which measures 6 x 6 x 15 a spider is sitting on one of the 6 x 6 walls 1/2m from the ceiling and 5 1/2m from the floor and 3m from the side walls. On the opposite 6 x 6 wall a fly is sitting 1/2m from the floor and 5 1/2m from the ceiling and 3m from the side walls. Prove that the shortest path between the two is 21m. The path can use any walls, ceiling, and floor, but can not jump out into space.”

Problem creator: Henry E Dudeney.

By the time I’d grown up, I naturally supposed that I’d be grown up. – Eve Babitz

The mid-points of three of a cube’s edges are joined as shown above. How big is the angle of the broken line?

Life must be understood backwards; but… it must be lived forward. – Soren Kierkegaard

there once was a set

that was so sad

sad? you ask

sad indeed

you see

the number of elements

in the set

was not in the set itself!

like 3 in {2, 3, 7}

or even 1 in {1}

now I wonder

and you may too

how many subsets of {1, 2, 3, … , n}

are sad

and what to do

Problem source: Mathcamp 2009 Qualifying Quiz.

Clothes make the man. Naked people have little or no influence on society. – Mark Twain

Steven Strogatz is a professor of applied mathematics at Cornell University. In 2007 he received the Communications Award, a lifetime achievement award for the communication of mathematics to the general public. He previously taught at the Massachusetts Institute of Technology, where he received the E.M. Baker Award, an institute-wide teaching prize selected solely by students. “Chaos,” his series of 24 lectures on chaos theory, was filmed and produced in 2008 by The Teaching Company. He is the author, most recently, of “The Calculus of Friendship,” the story of his 30-year correspondence with his high school calculus teacher. In this series, which appears every Monday, he takes readers from the basics of math to the baffling.

Link to his weekly articles: From Fish to Infinity, Rock Groups, The Enemy of My Enemy, Division and Its Discontents, The Joy of X, Finding Your Roots, Square Dancing.

The SET is a game where each card has four features: colours (red, green, purple), symbols (squiggles, diamonds, ovals), shading (solid, striped, outlined), and the number of symbols (one, two, three).

Choose the card from the bottom row that will complete the SET in the top row.

What is a SET? you cry. Glad you asked!

A SET consists of three cards were the features are all the same or all different.

Play it here.

(Not drawn to scale.)

In the grid above choose three points that make a triangle. Calculate its area. How many areas are possible?

The distance between a point and its neighbours left, right, up, and down is one light year.

Problem source: Andrew Adler.

There is a great deal of difference between an eager man who wants to read a book and the tired man who wants a book to read. – G K Chesterton