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Problems from Another Time

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

Nuts Over Counting
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?
Two Balls, No Strikes!
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.
Mystery Number
What number is that, which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
Under Siege
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.
Japanese Temple Problem 2
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
Area of an Equilateral Triangle
Suppose the area of an equilateral triangle be 600. The sides are required.
A Triangular Problem
In a right triangle, having been given the perimeter, a, and the length of the perpendicular from the right-angled vertex to the hypotenuse, b, it is required to find the length of the hypotenuse.
A Grinding Stone
Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
Mutually Tangent Circles
Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.
Pennies for the Poor
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?

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