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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 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?
There is a garden is the shape of a rhombus whose side is 768.52 feet. Within the garden is an inscribed square flower bed whose side is 396 feet. What is the area of the garden?
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.
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?
A man and his wife drink a barrel of wine at different rates. Find the rate it takes both of them together to drink the wine.
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?
Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
Determine the greatest cylinder that can be inscribed in a given cone.
A father wills his estate valued at $40, 000 to his three children. Before the settlement one of the children dies. What should the other two receive?
A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.

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