# Problems from Another Time

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

I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
A woodcutter starts to fell a tree 4 feet in diameter, and cuts half way through. One face of the cut is horizontal, and the other face is inclined to the horizontal at an angle of 45 degrees. Find the volume of the wood cut out.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
I found a stone but did not weigh it; after I added to it 1/7 of its weight and then 1/11 of this new weight, I weighed the total at 1 mina. What was the weight of the stone?
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.
A man agreed to pay for 13 valuable houses worth $5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last. A horse halving its speed every day runs 700 miles in 7 days. A father left$20,000 to be divided among his four sons ages 6, 8, 10, and 12 years respectively so that each share placed at 4 1/2 compounded interest should amount to the same value when its possessor becomes the age 21.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students