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Classic Problems from the Dr. Math Archives

Age Word Problems
Al's father is 45. He is 15 years older than twice Al's age. How old is Al? Karen is twice as old as Lori. Three years from now, the sum of their ages will be 42. How old is Karen?

Birthday Probability
What if somebody offered to bet that at least two people in your math class had the same birthday? Would you take the bet? How large must a class be to make the probability of finding two people with the same birthday at least 50%?

Boy or Girl?
In a two-child family, one child is a boy. What is the probability that the other child is a girl? What if the older child is a boy?

Camel and Bananas
What's the maximum number of bananas the camel can transport across the desert?

Coin Problems
Tony has 11 more nickels than quarters. How many coins does he have if the total value of his coins is $2.65?

Doubling Pennies
Which is more, a million dollars or a penny doubled every day?

Grazing Animals
A cow/goat/donkey is tethered to a barn in or a fence around a field...

Liars and Truthtellers
What question should the princess ask the natives to find out the right road to take?

Missing Dollar
The motel bellboy decides to keep the money for himself - where's the missing dollar?

Monty Hall (Three Doors)
Let's Make a Deal: If you're shown a goat behind the second door, should you stay with your first choice or switch?

Three Houses, Three Utilities
You are to draw a line from each house to each utility, without the lines ever crossing. Can you connect the houses to the utilities?

Tower of Hanoi
How many moves will it take to transfer n disks from the left post to the right post?

Two Trains
Two trains leave different cities heading toward each other at different speeds. When and where do they meet?

Two Trains and a Fly
Two trains 150 miles apart travel toward each other along the same track, the first train at 60 mph, the second at 90 mph. A fly buzzes goes back and forth between the two trains until they collide. If the fly's speed is 120 mph, how far will it travel?

See also Isaac Reed's Famous Problems in the History of Mathematics:

For more math and logic problems arranged by level of difficulty and with answers and solutions, see Shack's Math Problems by Michael Shackleford.

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