1

Part of 1991 National High School Mathematics League

Problems(2)

Count the Triangles

Source: 1991 National High School Mathematics League, Exam One, Problem 1

The number of regular triangles that three apexes are among eight vertex of a cube is

\text{(A)}4\qquad\text{(B)}8\qquad\text{(C)}12\qquad\text{(D)}24

geometry3D geometry

Count the Number of Arithmetic Sequences

Source: 1991 National High School Mathematics League, Exam Two, Problem 1

S=\{1,2,\cdots,n\}

A

is an increasing arithmetic sequence (at least two numbers), and all numbers are in

S

. Also, we can't add any number in

S

A

without changing its tolerance. Find the number of such sequence

A

arithmetic sequence