### Brain Teasers

# Coin on a Chessboard

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability

If a chessboard is the size of 80cm, and you throw a coin onto it of diameter 2cm. The centre of the coin falls somewhere within the 64 squares. What is the probability that it lands fully on a white square?

### Answer

For the coin to fall within a white square, it (its centre) must fall into a smaller area inside a white square. This smaller area will also be a square with its length 2cm shorter than the 10cm white square. (If the coin falls at the very edge of the white square, its centre will be on the edge of this smaller white square; the border of this square will be 1cm away from the border of the larger square). So it must land within this area = 64 square cm.The area of a white square is 100 square cm = 64/100, but only every 2nd square is white, so the answer = 32/100.

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## Comments

Good one... once I got over the thought that it may have been a riddle - heh, good thing these categories. Once I knew it was mathematical, it fell into place.

Not to be too picky, but that would be true only if the puzzle stated, "The ENTIRE coin falls within one of the 64 squares." The puzzle currently says the "CENTER" of the coin will land within one of the 64 squares. This means that the coin can land anywhere on the board except for the center of it landing exactly on a line. Cool teaser though - sorry I had to get critical.

Incorrect, sack. If the question stated that the entire coin landed in one of the 64 squares, the answer would obviously be 1/2, since half the squares are white. It is important in this teaser that the coin's center can land anywhere on the board with equal probability.

this will sound wrong and dirrty but i agree with bender! + isn't there a simpler explanation!

Another good one from cath. Well thought out and the conditions were clear and precise. I liked it!

The question seemed to be a bit ambiguous, making it uncertain if the board was 80 centimeters squared or 80 centimeters on a side. If it is 80 centimeters on a side, each square would be 10 cm (about 4 inches) square, rather a huge chessboard, I would think.

Interesting teaser though.

Interesting teaser though.

That was fun, did it in about 60 seconds, I posed a similar problem a long time ago on here with a square of side 100 cm, fully containing 2 smaller squares each of side 17 cm. The question was to find the probablity they touch or overlap, I had a nice solution using triangles

My eyes are bleeding from seeing 32/100 instead of 4/25!!!

I mean 8/25 X_X

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