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Problems from Another Time

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

The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.
 
Given a number, take 1/3 of the number away from itself and also remove 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.
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. What is the smallest number of nuts he could have?
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.
What number is that, which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
There are two numbers whose sum equals the difference of their squares.

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