In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

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In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.

Problems from a 15th century French manuscript, including one with negative solutions

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.

This is page 167 from the Exercitationes mathematicae (1657) of Frans van Schooten (1615-1660). This book contained a collection of mathematical construction problems, among much else. It was one of the books read by Isaac Newton while he was a student at Cambridge University and helped to introduce him to modern mathematics. On this page we see a construction enabling one to find the distance across a river.

Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.

In a given square, inscribe 4 equal circles so that...

Given the frustum of a circular cone with height h.

Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.