Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 2*97=194 so S=1+9+4=14. If n=4444 then 2*4444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.

Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 297=194 so S=1+9+4=14. If n=4444 then 24444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 7 Three students wrote the number 678.23 in different ways. Crystal: Dakota: 6 hundreds, 7 tens, 8…

A: According to bartleby guidelines we do only first question and rest question can be reposted…

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

Q: if these five numbers form a pattern such that the differernce between each pair of numbers is the…

Q: iven that 120=2^3 *3*5 and that n=120*108 write n as a product of powers of its prime f

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: The total curb weight of a truck, a car A, and a car B is 11,250 lb. The weight of car A is 15 lb…

A: Given,The total weight of a truck, car A and car B is 11,250 lb. The weight of car A is 15 lb less…

Q: An identity thief is trying to break into someone's computer that is protected by a 4-digit passcode…

Q: Using the digits 2 through 9, find the number of different 6-digit numbers such that: a. Digits can…

A: Answer:- Given digits are - 2,3,4,5,6,7,8,9 Total number of digits= 8

Q: How many times does the the exact number 123456 appear in the first one million digits of PI

A: PI—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle…

Q: Suppose we want to form four-digit numbers using the set of digits {0,1, 6, 7, 9}. For example, 9071…

A: The first number can be selected in 4 ways. [ Any number from {1,6,7,9} ] The second number can be…

Q: How many ways can you have a 6-digit passcode on your phone if you start with a 9 and none of the…

A: We need to find the number of ways to have a 6-digit passcode, given that the first digit is 9 and…

Q: 1+1+5215+5102

Q: If n is a natural number, what does bn mean? Give an example with your explanation?

A: Given: n is a natural number. Then bn means, multiply a number b with itself n times.

Q: A 16-bit string is a sequence of 16 symbols, each symbol a 0 or a 1. How many 16-bit strings are…

A: A bit string is a sequence of symbols, each symbol a or a We have to find the possible number of…

Q: Assume that we have numbers from 0 to 9 in a small box (0,1,2,3,4,5,6,7,8,9); there is only one from…

A: Solution:-To determine the number of 5-digit numbers that can be generated respecting the given…

Q: how many 7 digit phone numbers can be formed in an area code, if the symbols 0 and 1 can not be used…

A: We consider that each digit is selected independently of the others. The first digit can be any of…

Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers no repeatation odd numbers: last digit must be odd.…

Q: What is the inverse of 16 modulo 43 i.e. which number a has the property that 16*a has the remainder…

A: From question we have to find the inverse of 16 modulo 43. i.e 16*a mod(43)=1 It can also be…

Q: A briefcase lock opens with the correct 4 digit code. If the digits can be any number from 1-9 with…

A: Given: Digit is from 1 to 9 Unit must be = 3,6,9 that mean 1 of these 3 Other 3 are from 1-8 ,…

Q: Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one…

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

For some particular website, the password must start with one of the letters a b or c. Then there must be 6 or more characters and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible. So far I have 3*36*36*36*36*36*36=
Find the number of different 7-digit numbers which can be formed from the seven digits 4, 4, 7, 9, 9, 9, 2 in each of the following cases.a. The odd digits are together and the even digits are together.b. The 4s are not together
How many different three-digit numbers can be formed using the digits 1, 4, 5, and 9 without repetition? For example, 114 is not allowed. The number of different three-digit numbers is.
a. On each of four consecutive plays in a football game, a team lost 8 yards. If lost yardage is interpreted as a negative integer, write the information as a product of integers and determine the total number of yards lost. b. If Jack Jones lost a total of 55 yards in 11 plays, how many yards, on average, did he lose on each play?
You need to create a four digit code. You can use the digit 035. The first is it cannot be zero. And the digits are not allowed to repeat. How many such codes are possible?
Lizzie came up with a divisibility test for a certain number m 1: · Break a positive integer n into two-digit chunks, starting from the ones place. (For example, the number 354764 would break into the two-digit chunks 64, 47, 35.) · Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 64 – 47+ 35 = 52.) Find m, and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m). %3D
Evaluate the expressions 32 4/5 and 81 1/4
How many ways can you arrange 25 items, 14 of which are distinct and 11 are identical. Express your answer in scientific notation to 3 significant digits.
What is the first common multiple of 5 and 7 that is even num
(c) Suppose x and y are both solutions to the pair of congruences. What is the smallest possible positive value of x - y? (d) Briefly explain your answer to part (c).