# 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...
A farmer sold a team of horses for $440, but did not receive his pay for them until 1 yr, 8 mo after the sale. He had at the same time another offer of$410 for them. Did he gain or lose by the sale and by how much, money being worth 6%/yr?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
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 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.
X, Y and Z hired a pasture for the season for \$90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
A horse halving its speed every day runs 700 miles in 7 days.
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?