# Problems from Another Time

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

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
Given the frustum of a circular cone with height h.
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?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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?
An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
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.
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.
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?