Let
What is the largest number of elements in
Ten circles are marked on the circle. How many non-closed non-self-intersecting nine-point broken lines exist with vertices at these points?
How many nine-digit numbers exist, the sum of the digits of which is even?
Prove the validity of the following formula of Newton’s binom
Calculate the following sums:
a)
b)
c)
In the expansion of
Here is a fragment of the table, which is called the Leibniz triangle. Its properties are “analogous in the sense of the opposite” to the properties of Pascal’s triangle. The numbers on the boundary of the triangle are the inverses of consecutive natural numbers. Each number is equal to the sum of two numbers below it. Find the formula that connects the numbers from Pascal’s and Leibniz triangles.
Draw all of the stairs made from four bricks in descending order, starting with the steepest
A frog jumps over the vertices of the triangle
How many ways can it get from
The segment