You write numbers on each square in a chessboard such that the number on a square is equal to the average of the numbers in all the squares adjacent to it (two squares are adjacent if they share a common line). Show that all the numbers in all squares are equal - An old puzzle I remembered.
Monthly Archives for December, 2013
One hypothesis is that the energy requirements of the human body cannot be met via photosynthesis only. The reason plants don't move is that they don't get enough energy from photosynthesis. Is this hypothesis correct? Google for appropriate data, and see if photosynthesis can produce the 2000kcal of energy that an average human needs everyday.
This is not a puzzle, rather an interesting concept. A Menger sponge is defined as follows: 1. Take a 1x1x1 cube and divide it into 27 smaller cubes like a Rubix cubes. 2. Remove the small cubes in the middle of each face, and the small cube in the center. We are left with 20 cubes. 3. Repeat steps 1,2 for each smaller cube. 4. Keep repeating this process … Continue reading the story "Menger sponge"
A game show host places 3 coins: 1 bronze, 1 silver and 1 gold. He tells you that if you tell a true statement, you will get one of the three coins. If you lie however, you will not get any coin. What statement should you make to guarantee you get the gold coin? - via Richard Wiseman blog
A library that has every book in the world won't be so useful. Google is probably more useful. The usefulness of a library is determined by how soon you can get information you want, not by how many books are in the library. See why for yourself via this Quora article.
Without using log tables or calculators, show that . - via Moscow math Olympiad problems
A is a 300 x 300 matrix with 17 on the diagonal, and the rest of the entries being 11. What is det(A)? Hint: It is sometimes easier to solve a more difficult problem. - via Sudeep Kamath
In computer graphics applications you have a bunch of objects in 3d space. You like to do collision detection. For example, if a bullet hits you or the enemy, or if you punch an enemy, you like to know if there is a collision. All objects are composed of cuboids and 3d ellipsoids. Assuming there are n objects how can you quickly determine which pair … Continue reading the story "Collision detection"
The image below represents a valid equation formed by matchsticks. Can you move one matchstick such that the equation is correct?