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Problems from Another Time

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

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?
One person possesses 7 asavas horses, another 9 hayas horses, and another 9 camels. Each gives two animals away, one to each of the others.
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?
There are two numbers whose sum equals the difference of their squares.
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?
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.