The agent obtained some information concerning a new confidential algorithm for encrypting governmen...: ответ на тест 1056136 - Информатика

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 number 75110 in the radix number system with q-base is represented as follows: 11100110011q the base of this system will be the following …

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.

The logical structure from the picture

corresponds to the following symbol …