The number of various non-degenerate triangles the side lengths of which are whole numbers with the ...: ответ на тест 1055480 - Информатика

The number of various non-degenerate triangles the side lengths of which are whole numbers with the perimeter of  is as follows …

There are N triangles given by six whole numbers, vertexes of a triangle  . The triangles are allocated in the space with the following coordinates: . Thus the source data are as follows:
.
The number of dots with integral coordinates located within more than two triangles including their sides is as follows …

There are N triangles given by six whole numbers, vertexes of a triangle  . The triangles are allocated in the space with the following coordinates: . Thus the source data are as follows:
.
The number of dots with integral coordinates located within more than two triangles including their sides is as follows …

The sequence of natural numbers  from  to  is represented without any spaces between them. The decimal sequence obtained is sorted descending the one-digit numbers corresponding to the decimals. For example for   and  the ordered sequence will have the following representation:
98765211110. For  and  the sequence will contain as many “7” digits as____, the first of which is in position with ordinal number _____.
Give your answer in two numbers separated by a comma. For example for  and  in the sequence there will be 19 digits of 7 beginning from position number 39. Thus the result is written as 19,39

Some  cryptographic algorithm requires matching natural numbers that can be represented as a sum of two different prime numbers using more than k ways, thus all the three numbers (the unknown and two summands) should have the same number of digits. For example: number 30 matches k-1 case as it can be represented as follows:  and . Number 32 doesn’t match as it can be represented by only one sum: 19+13.
The quantity of 4-digit  decimals for k= 10 is …

Little Piggy decided to categorize his archive containing a lot of different format files. There are pictures, videos, audio, documents, e-tables, documents templates, Web-pages with different file extensions, text of programs in different programming languages and even unknown content files with .hrj extension. Altogether there are 1001111 files. At first Little Piggy decided to move all the pictures into one folder. Thus he selected 5 filtering masks for file names. Most files will be filtered when using the following mask …
Let’s presume that the number of files of every format is relatively similar.