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Problem description Progress
ID 38812. How many different numbers and which ones?
Темы: Number systems   

Value of expression \(11 \cdot 15^{65} + 18 \cdot 15^{38} – 14 \cdot 15^{17} + 19 \cdot 15^{ 11} + 18338\) was written in base 15. 
Print in the first line, separated by one space, the digits in ascending order that occur in the resulting number (for digits greater than 9, use large English letters). The second line contains the number of different digits used to write the resulting number.

ID 39050. Let's count the numbers - 03
Темы: Number systems    USE   

The value of an arithmetic expression

\(3 \cdot 4^{47} + 4 ^{32}- 4^{25} -2 \cdot 4 ^{20}-8\)
written in the number system with base 16. How many digits 'F' contained in this post?

ID 39049. Let's count the numbers - 02
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 4^{47} + 2 \cdot 4 ^{39}+3 \cdot 4^{37 } + 2 \cdot 4^{36}+3 \cdot 4^{32}+1\)
written in the number system with base 8. How many significant zeros are in this entry?

ID 39048. Let's count the numbers - 01
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 4^{39} + 2 \cdot 4 ^{36}- 2 \cdot 4^{32 } - 4^5-2 \cdot 4^2+1\)
written in the number system with base 16. How many digits 'F' contained in this post?

ID 39051. Let's count the numbers - 04
Темы: USE    Number systems   

The value of an arithmetic expression

\(2 \cdot 4^{47} + 2 \cdot 4 ^{44}- 2 \cdot 4^{39 } - 2 \cdot 4^{37}-3 \cdot 4^{36}+1\)
written in the number system with base 4. How many significant zeros are in this entry?

ID 39053. Let's count the numbers - 06
Темы: USE    Number systems   

The value of an arithmetic expression

\(2 \cdot 4^{84} + 3\cdot4 ^{42}- 2\cdot4^{34}+ 2 \cdot 4^{17}+3\cdot 4^{3} +16\)
written in the number system with base 4. How many 3 digits does this entry contain?

ID 39052. Let's count the numbers - 05
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 4^{84} + 4 ^{83}- 4^{63} - 3 \cdot 4 ^{42}+4^{40} - 4^{38}+3\)
written in the number system with base 8. How many 7 digits does this entry contain?

ID 39085. Let's count the numbers - 07
Темы: USE    Number systems   

The value of an arithmetic expression

\(2 \cdot 8^{99} + 2\cdot8 ^{30}- 2\cdot8^{85} - 2 \cdot 8^{15}+3\cdot 8^{5} -8^3- 2 \)
written in the number system with base 8. How many 7 digits does this entry contain?

ID 39086. Let's count the numbers - 08
Темы: USE    Number systems   

The value of an arithmetic expression

\(2^{234} + 2 ^{100}- 2^{43}- 2^{35}+2 ^{8} -129\)
written in the number system with base 16. How many 0 digits does this entry contain?

ID 39087. Let's count the numbers - 09
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 8^{112} - 2\cdot8 ^{78}+4\cdot8^{63}- 2 \cdot 8^{35}-8^{8} -52\)
written in the number system with base 8. How many 7 digits does this entry contain?

ID 39088. Let's count the numbers - 10
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 7^{112} - 2\cdot7 ^{78}+4\cdot7^{63}- 2 \cdot 7^{35}-7^{8} -52\)
written in the number system with base 7. How many significant digits of 0  does this entry contain?

ID 39357. Number in binary system
Темы: Number systems   

Input
The program receives a natural number as input - N

Imprint
Display the representation of the number in binary form, in which the digits of the number are written in reverse order, that is, from the end.
 

Examples
# Input Output
1 6 011

ID 39358. Number in octal number system
Темы: Number systems   

Input
The program receives a natural number as input - N

Imprint
Display the representation of the number in octal notation, in which the digits of the number are written in reverse order, that is, from the end.
 

Examples
# Input Output
1 250 273

ID 39359. Number in hexadecimal number system
Темы: Number systems    Computer science   

Input
The program receives a natural number as input - N

Imprint
Display the representation of a number in hexadecimal notation, in which the digits of the number are written in reverse order, that is, from the end. To represent numbers from 10 to 15, use capital English letters from  'A' to 'F'.
 

Examples
# Input Output
1 250 AF

ID 39360. Converting a number to decimal number system
Темы: Number systems    Computer science   

Write a program that converts the number N from base r to decimal.

Input
The program receives two natural numbers as input: and r (2 <= r <= 9). It is guaranteed that the number N is the correct representation of the number in the number system with the base r (that is, it contains the numbers from 0 to r- 1).

Imprint
Display the number in decimal notation.
 

Examples
# Input Output
1 100 2 4

ID 39361. Pair with the highest amount
Темы: Number systems    Nested Loops   

The program input receives pairs of numbers: a natural number N and the base of the number system r, in which the number N is written. The sign of the end of the input is the pair 0 0. Print a pair of numbers with the maximum sum on the screen. Display numbers in decimal notation. In this problem, by a pair we mean two numbers located side by side.

Input
The input is an unknown number of lines. Each line, except the last one, contains 2 numbers: N (1 <= N <= 107) and r (2 <= N <= 9). The last line contains a pair of 0 0 (a sign of the end of input).

Imprint
Print the answer  a pair of numbers with the maximum sum. If there are several such pairs, print the first one.
 

Examples
# Input Output Explanation
1 3 5
21 4
1 3
18
23
0 0
3 9 In the source data we have the following numbers
35, 214, 13, 18, 23< br /> The pairs are as follows:
(35, 214), (214, 13), (13 , 18), (18, 23)
The pair with the highest sum (35, 214). In decimal notation, these are numbers (3, 9)
Answer: 3 9

ID 39651. Error
Темы: Number systems   

The value of an arithmetic expression

\(3 \cdot 4^{8072} - 2 \cdot 16^{512} - 3 \cdot 8^{128 } - 1024\)
written in base 4 number system. How many digits 3 are there in this notation?
 

ID 39652. Error
Темы: Number systems    Arithmetic operations   

The value of an arithmetic expression

\(3 \cdot 4^{8072} - 2 \cdot 16^{512} - 3 \cdot 8^{128 } - 1024\)
written in the number system with base 16. How many significant even digits does this notation contain?

Even digits in hexadecimal: 0, 2, 4, 6, 8, A, C, E.

ID 39653. Error
Темы: Number systems    Arithmetic operations   

The value of an arithmetic expression

\(3 \cdot 4^{8072} - 2 \cdot 16^{512} - 3 \cdot 8^{128 } - 1024\)
written in base 16 number system. How many adjacent pairs of digits "FC" contained in this post?

ID 39654. Error
Темы: USE    Number systems   

The value of an arithmetic expression

\(3 \cdot 8^{112} - 2\cdot8 ^{78}+4\cdot8^{63}- 2 \cdot 8^{35}-8^{8} -52\)
written in the number system with base 8. How many digits other than 7, are in this entry?

ID 39655. Error
Темы: USE    Number systems   

The value of an arithmetic expression

\(2 \cdot 4^{84} + 3\cdot4 ^{42}- 2\cdot4^{34}+ 2 \cdot 4^{17}+3\cdot 4^{3} +16\)
written in the number system with base 4. How many adjacent numbers "20" contained in this post?

ID 39656. Error
Темы: USE    Number systems   

The value of an arithmetic expression

\(25^{4848} - 2\cdot25 ^{4090}- 2\cdot5^{4556}- 4 \cdot 5^{2276}-5^{4404} -5^{4313}+13320\)
written in the number system with base 5. How many adjacent pairs of numbers "41" contained in this post?

ID 39806. DV-2022
Темы: USE    Number systems   

The value of an arithmetic expression

\(3\cdot 16^{2018} - 2\cdot 8 ^{1028}- 3\cdot4^{1100} - 2^{1050}-2022\)
written in the number system with base 4. How many triples are there in this entry?

ID 40169. June-2
Темы: USE    Number systems   

The value of an arithmetic expression

\(3\cdot 216^{18} - 2\cdot 36 ^{10}- 3\cdot6^{9} - 2\)
written in the number system with base 6. How many 5 digits are in this entry?