,
an integer, that lie within the polygon is equal to the sum of the lengths of the segments of lines of the form 
,
an integer, that lie within the polygon.
,
,
intersects a circle at exactly two points 
and 
.
is extended beyond 
such that 
.
intersect at the point 
.
is cyclic. (4)
ascertain whether among its first 
terms there is a number that ends with four zeros.
straight lines in general position are drawn on the plane. Prove that among the parts into which they divide the plane, there are at least 
triangles
and 
such that 
pupils is organised into 
clubs , so that each club contains 
pupils and no two clubs have the same composition. Prove that there are two clubs which have exactly one common member.
of its volume is below the water level, while more than half of its surface area is above the water level?
to 
Y by
The cells of a 
table contain non-zero numbers. It turned out that all 
hundred-digit numbers written horizontally are divisible by 11. Could it be that exactly 
hundred-digit numbers written vertically are also divisible by 
?
table contain non-zero numbers. It turned out that all 
hundred-digit numbers written horizontally are divisible by 11. Could it be that exactly 
hundred-digit numbers written vertically are also divisible by 
?This post has been edited 1 time. Last edited by parmenides51, Sep 27, 2024, 4:13 PM
