Complexity of Ken Ken Game

I came across this puzzle named Ken Ken. It is Sudoku-type puzzle with arithmetic constraints. Here is a complexity question :

• Is solving n x n Ken Ken puzzle NP-complete ?

NP-completeness results are known for similar games like Sudoku. Here is a paper on mathematics of Septoku. Here is David Eppstein's list of games with complexity results.

Train Probability Puzzle

The probability of observing a train in 30 minutes on a track is 665/729. What is the probability of observing a train in 5 minutes ?

Hint : Shoot for an elegant solution.

Polynomials difference puzzle

Here is a cute puzzle about difference of polynomials.

Common Puzzles

Most of my friends are geeks. So when we get together on a friday night (or) driving to a conference, we don't talk about politics, movies or celebrities. Instead we throw math puzzles at each other. Here are some of the common puzzles I ran into....

• The Banana-eating Camel : You have 3,000 bananas that must be transported across a desert that is 1,000 kilometers wide. You have a camel that has a 1,000 banana capacity. However, the camel must eat one banana for each kilometer that it walks. What is the largest number of bananas that can be transported across the desert?
  

• 12 Balls : There are 12 balls. They all look alike but one of them is faulty; it weights differently. It is not known, if this ball is heavier or lighter than the other balls. How to find the faulty ball by three weighs on a simple balance ?

• Linked Lists : You are given a pointer to the head of a singly linked list that might (or might not) have a loop somewhere (i.e., an element pointing back to an element). The length of the list is finite, but unknown. Devise an algorithm that detects if there is a loop. You must use only a constant amount of memory space and not destroy the list.

• Two Integers : I'm thinking of two integer numbers, each if them is more than 1 and their sum is less than 100. I tell my friend A the sum of these two numbers, and another friend B, product of these two numbers. Then such a dialog took place:
  B: I can't determine what are these numbers.
  A: Ah, i knew you wouldn't be able to do this.
  B: Oh, then i know what they are!
  A: Oh, then i know them too!
  
  Can you determine the numbers?

• Stick triangle : A stick is broken at random into three pieces. What is the probability that the pieces can form a triangle?
  
  

These are the easiest ones (the appetizers). Have fun solving them. I will add more difficult puzzles in future posts...

Tiling chessboard by L-shaped trominoes

Can you cover all but one square of an n x n chessboard by L-shaped trominoes?

Claim : If n is a power of 2, you can always do it !!

Have fun proving this !!

25 Horses Puzzle

There are 25 horses and only five tracks in a race (i.e., you can race 5 horses at a time). There is no stop clock !! Assume that there are no ties.

1: What is the minimum number of races needed to determine the 3 fastest horses in order from fastest to slowest ?
2: ..... to find out the fastest one ?
3: ..... to rank all of them from fastest to slowest ?
4: ..... to find the top k fastest horses ?