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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

What is the value of X...
If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
Assume that the human population after the flood was 6 and that 200 years later the population was 1,000,000. Find the annual growth of the population.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

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