Вопрос № 1055487 - Информатика

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.

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Computers store information on disks in files. A file is a collection of related information such as a computer program or the text of a letter.
Each file is given a unique name, and each filename is stored in a directory. To find out about the files in a directory, use the MS-DOS command DIR.
When referring to a file, you must use a file specification. This consists of a pathname, a filename and an extension (if there is one). As an example, to reference a file on drive B: called FRED.BAS (where the default drive is ‘A’) the correct file specification would be:
B:\FRED.BAS
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How do you find out about the files?

The agent obtained some information concerning a new confidential algorithm for encrypting governmental communication of the potential enemy. However, having almost failed his mission, he had to eat the secret information and  rinse it down with a glass of Coca-Cola. Upon return to the base the data were retrieved from the stomach and partially restored. The basis of encryption was the conversion of number  into a numerical system with a q based number. The base of a number system was lost. However it was found out that the base of the number system was a natural number less than 100 and the number obtained as a result of  conversion contained two 5, one 7 and one 9. Other numbers were permanently lost.  The base of a number system used to convert the operand  is …

In the long-long warehouse, on the long-long shelf there are some heads of cheese stored. Each cheese head is consistently numbered by natural number beginning from 1. One night the first hamster got into a warehouse and  ate up every second cheese beginning from  the second one.  The following night the second hamster  got into a warehouse and ate every second of the remained cheese heads beginning from the first one. After that three rats got into a warehouse and ate every third of the remained cheese heads, beginning from the third. Then the first hamster got hungry and decided to eat some cheese again so it got into a warehouse again and ate every second cheese, beginning from the second, then the second  Hamster ate up every second cheese, beginning from the first, then three rats again… Eventually there was only one cheese head left. Animals decided to leave it not to reveal their presence. On condition that there originally were 123456 heads of cheese, the number of the last cheese head left was …

Let’s suppose that a palindromic number or numeral palindrome is a number of at least two characters  that remain the same when its digits are reversed. For example number 1221 is a palindrome while number  isn’t.
Let’s call a palindrome2 a Base 10 (decimal) palindrome the Base -2 (binary) representation of which is also a palindrome. For example number 33 is a palidrome2 since its Base-2 (binary) representation (100001) is also a palindrome. In the first million of natural numbers there will be so many as ____ palindrome2.

The algorithm of converting a certain  sequence of symbols is set. At every stage of the algorithm the following operations are carried out:
1) at the end of the sequence before stepping its copy in the reversed order is written (symbols are written in the reversed order);
2) at the end of the sequence obtained the quantity of symbols that equals the stepping number of the algorithm is removed.
The results of the first two steps are given for 1234 input sequence:
1: 1234432
2: 123443223443
As for the input sequence of ALGORITM symbols after the 10th step of transformation there will be symbol _____ on position 1024.