Problems – Page 2 – We Solve Problems
Filter Problems
Showing 21 to 40 of 2116 entries

#### Linear recurrent relations , Periodicity and aperiodicity

In a row there are 1999 numbers. The first number is 1. It is known that each number, except the first and the last, is equal to the sum of two neighboring ones.
Find the last number.

#### Central angle. Arc length and circumference , Chords and secants (other) , Isosceles, inscribed, and circumscribed trapeziums , Pigeonhole principle (finite number of poits, lines etc.) , Regular polygons , Two tangent lines to a circle, intersecting at a particular point

In a regular shape with 25 vertices, all the diagonals are drawn.
Prove that there are no nine diagonals passing through one interior point of the shape.

#### Integer and fractional parts. Archimedean property , Pigeonhole principle (angles and lengths)

Some real numbers $a_1, a_2, a_3,…,a _{1996}$ are written in a row. Prove that it is possible to pick one or several adjacent numbers, so that their sum is less than 0.001 away from a whole number.

#### Odd and even numbers , Polynomials with integer coefficients and integer values , Rational and irrational numbers

n numbers are given as well as their product, p. The difference between p and each of these numbers is an odd number.
Prove that all n numbers are irrational.

My Problem Set reset
No Problems selected