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This annulus has been formed from two concentric circles. A chord of length t of the larger circle is then drawn tangent to the inner circle.
If you only know the value of t, can you calculate the area of the annulus?
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French mathematician Joseph Bertrand posed the following problem in 1889:
You have 3 identical boxes, each containing 2 coins: the first box 2 gold coins, the second box 2 silver coins, and the third box 1 gold and 1 silver coin.
Your friend shuffles the boxes at random. Then, you choose a box and pull a coin out of it, and it's gold.
What is the probability that the other coin in the same box is also a gold coin?
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I have a square puzzle consisting of 10×10=100 pieces.
If I pick two pieces at random, what is the probability that they fit together, i.e. they lie next to each other in the puzzle?
If the probability can be written as ba with coprime positive integers a and b, give your answer as a+b.
Details and Assumptions:
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Four congruent semicircles are packed into a square.
What proportion of the square is filled?
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The sum of the ages of my five nieces is 47. Their ages are positive integers, and any two of them have a common divisor greater than 1.
How old is the eldest?
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