Chess Board Puzzle

A semi-infinite chess board (vary from zero to infinity in both dimensions) with counters in the three bottom left squares, as shown in the below figure.



How to move: If the squares above and to the right are free, a counter can be removed and replaced by two counters, one in the square above and one in the square to the right – check below



Prove that it is not possible to leave the three bottom left squares empty.


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Black and White Squares Puzzle

Consider an n x n chessboard, where each square is arbitrarily chosen to be either black or white. Your goal is to make all squares in the chessboard white. At each step, you are allowed to “switch” a square, but each switch will toggle not only the particular square being switched, but also the 4 squares that are adjacent to it: Two vertically up and down and two horizontally up and down the square being switched.
Note : At corners only 4/3 squares are toggled, while at the center all 5 squares are toggled.

How you can make the entire chessboard white.
Found at : http://puzzletweeter.com

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Swap two Variables

Swap two Variables (integers) without using a temporary variable

How to swap two integer values without using another variable?

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The Mysterious Murder Of Obadiah Squelch Puzzle

On 15th April 1892 Obadiah Squelch left his tomato processing factory for the last time: inside 200 cans labelled “Finest Tinned Tomatoes”. Who had committed this dreadful crime?

The Police brought in the Twig And Leaf Division (Special Branch) to investigate the case. It was a brief case.

Within minutes they had reduced the suspect list to six. After a further two hours they had ruled out suicide, so that left just five. Now they need your help to solve the mystery.

The suspect list:

DIRTY HARRY – The meanest bandit in the West
PERSIL PETE – The cleanest bandit in the West
BRANFLAKE BILL – Always on the go
DOMESTOS DEN – Just kills everything
VLOK SVAGEN – Vorsprung Durch Technic as they say in German

The Police returned to the scene of the crime with three chickens and a cockerel. They were the Four Hens-ic Scientists. Closer examination at the factory revealed a pool of red liquid around the tomato juice extractor. But it was already in the papers. It had been leaked by the press.

The headlines next day relayed the story to the world:

BRANFLAKE BILL AND VLOK SVAGEN RUIN OBADIAH’S DAY
O SQUELCH GOES DIRTY HARRY IN TROUBLE
SUN SAYS DEN AND PETE ARE INNOCENT
WHO CANNED OBADIAH? PERSIL PETE GETS CLEAN SHEET IN TRIAL

In fact, all the papers got it wrong. So who killed Obadiah Squelch?

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24 from 8,8,3,3

How will you get the answer 24 by only using the numbers 8,8,3,3.
You can use add, subtract, multiply, divide, logarithms, factorials, roots and parentheses.

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