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Problems from Another Time

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

Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
There is a number which when divided by 2, or 3, or 4, or 5, or 6 always has a remainder of 1 and is truly divisible by 7. It is sought what is the number?
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who receives double portions. What is the share of each?
A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
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?

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