Place four points in the plane such that the distance between any pair is >= 1 and the average distance between pairs is minimised.
Find a formula for the minimum average distance between pairs for four, five, six, …, n points.
I am sure this is a famous problem, but I don’t know its name or any results. I came to think of it when I was a dinner party as explained here.
Jill: How did you find the weather on your vacation?
Bill: I just went outside and there it was!
- Don Harshbarger
My friend and I sold all our sheep. I know, it is sad, but we needed the money to buy goats for $10 per goat. How much we got for the sheep? We got as many dollars per sheep as we had sheep. After buying the goats we had a few dollars left, so naturally we bought some rabbits. We ended up with an even number of animals we split evenly. My friend did not want any rabbits, so ,obviously, I wonder, how many dollars does he owe me?
Problem source: Dansmath.
Life is like stepping onto a boat that is about to sail out to sea and sink. - Shunryu Suzuki
The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2010 to John Torrence Tate, University of Texas at Austin, for his vast and lasting impact on the theory of numbers.
Which of the gentlemen above is a mathematician?
Only exceptionally rational men can afford to be absurd. - Allan Goldfein
The consecutive sides of a quadrilateral measures, let’s say, 6, 33, 47, and 34 light years. Determine the angle between the diagonals.
Problem source: MathCentral – Problem of the Month.
There is no end to education. It is not that you read a book, pass an examination, and finish with education. The whole of life, from the moment you are born to the moment you die, is a process of learning. – Jiddu Krishnamurti
Find the value of the question mark.
Problem source: Puzzletopia.
PUZZLETOPIA.net (puzzle + Greek, topos, place) is literally a place for puzzles. The noun, puzzle, means something that mystifies, baffles, bewilders, or perplexes, and it is almost poetic that the origin of the word, puzzle, is itself a mystery.
There is no reciprocity. Men love women women love children children love hamsters. - Alice Thomas Ellis