,
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?
red points divide a blue circle into 
to 
Y by
There is an 
table with 
cells containing ones and the remaining cells containing zeros. You can do this with the table the following operation: select the tap hole, subtract from the number in this cell, one, and to all other numbers on the same line or in the same column as the selected cell, add one. Is it possible from of this table, using the specified operations, obtain a table in which all numbers are equal?
table with 
cells containing ones and the remaining cells containing zeros. You can do this with the table the following operation: select the tap hole, subtract from the number in this cell, one, and to all other numbers on the same line or in the same column as the selected cell, add one. Is it possible from of this table, using the specified operations, obtain a table in which all numbers are equal?This post has been edited 1 time. Last edited by parmenides51, Sep 17, 2024, 11:53 AM
