Given a number of at most digits. We have to check if it is possible, after removing certain digits, to obtain a number of at least one digit which is divisible by 8. We are forbidden to rearrange the digits.

Property of the divisibility by eight : number can be divided by eight if and only if its last three digits form a number that can be divided by eight. Thus, it is enough to test only numbers that can be obtained from the original one by crossing out and that contain at most three digits i.

Method 1 Brute Force : We apply the brute force approach. We permute all possible single digit, double-digit and triple-digit combinations using an iterative ladder. If we encounter a single-digit number divisible by 8 or a double-digit number combination divisible by 8 or a triple-digit number combination divisible by 8, then that will be the solution to our problem. Method 2 Dynamic Programming : Though we have only digit numbers, for longer examples larger than that, our program might exceed the given time limit.

Thus, we optimize our code by using a dynamic programming approach. The value of dp is true if we can cross out some digits from the prefix of length i such that the remaining number gives j modulo eight, and false otherwise. For a broad understanding of the concept, if at an index, we find element modulo 8 for that index we put the value of.

For all other numbers, we build on a simple concept that either addition of that digit will contribute in formation of a number divisible by 8, or it shall be left out. Note: We also have to keep it in mind that we cannot change the order Now. Therefore, the overall complexity is O n. If you take a close look, the visited array will always have 10 fields and the map will always have the same size, hence space complexity will O 1time complexity will be O n for traversing string.

Attention reader! Writing code in comment? Please use ide. Skip to content. Related Articles. Example subsequences are16 and 8. Input : Output : No No subsequence is divisible by 8. Input : Output : Yes The subsequence is divisible by 8. If such permutation exists, the function. If such permutation. Python3 program to. Generating all possible. WriteLine "Yes". WriteLine "No".

Python3 program to find. Function takes in an array of numbers.Work fast with our official CLI. Learn more. If nothing happens, download GitHub Desktop and try again. If nothing happens, download Xcode and try again. If nothing happens, download the GitHub extension for Visual Studio and try again. Statement: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9.

The sum of these multiples is Statement: Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:.

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. Statement: A palindromic number reads the same both ways. Statement: is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Statement: By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is Find the thirteen adjacent digits in the digit number that have the greatest product. What is the value of this product?

Statement: The sequence of triangle numbers is generated by adding the natural numbers. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, Statement: Work out the first ten digits of the sum of the following one-hundred digit numbers. Statement: The following iterative sequence is defined for the set of positive integers:. It can be seen that this sequence starting at 13 and finishing at 1 contains 10 terms. Although it has not been proved yet Collatz Problemit is thought that all starting numbers finish at 1.

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is It is the first repdigit. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name. It is the smallest two-digit prime number in the decimal base.

The next prime is 13with which it comprises a twin prime. If a number is divisible by 11, reversing its digits will result in another multiple of As long as no two adjacent digits of a number added together exceed 9, then multiplying the number by 11, reversing the digits of the product, and dividing that new number by 11, will yield a number that is the reverse of the original number.

An sided polygon is called a hendecagon or undecagon. There are 11 regular and semiregular convex uniform tilings in the second dimension, and 11 planigons that correspond to these 11 regular and semiregular tilings.

### 11 (number)

In base 10, there is a simple test to determine if an integer is divisible by take every digit of the number located in odd position and add them up, then take the remaining digits and add them up. If the difference between the two sums is a multiple of 11, including 0, then the number is divisible by This technique also works with groups of digits rather than individual digits, so long as the number of digits in each group is odd, although not all groups have to have the same number of digits.

Another test for divisibility is to separate a number into groups of two consecutive digits adding a leading zero if there is an odd number of digitsand then add up the numbers so formed; if the result is divisible by 11, the number is divisible by This also works with larger groups of digits, providing that each group has an even number of digits not all groups have to have the same number of digits.

An easy way of multiplying numbers by 11 in base 10 is: If the number has:. In base 13 and higher bases such as hexadecimal11 is represented as B, where ten is A. In duodecimalhowever, 11 is sometimes represented as E and ten as T or X. There are 11 orthogonal curvilinear coordinate systems to within a conformal symmetry in which the 3-variable Helmholtz equation can be solved using the separation of variables technique. This works for any base, but the number eleven must be changed to the number represented as 11 in that base; for example, in duodecimal this must be done using thirteen.

In this case, this unique point is 15 On the seven-segment display of a calculator, 11 is both a strobogrammatic prime and a dihedral prime.

## 11 (number)

After Judas Iscariot was disgraced, the remaining apostles of Jesus were sometimes described as "the Eleven" Mark ; Luke and ; this occurred even after Matthias was added to bring the number to twelve, as in Acts [15] Peter stood up with the eleven New International Version. The New Living Translation says Peter stepped forward with the eleven other apostlesmaking clear that the number of apostles was now twelve.

Saint Ursula is said to have been martyred in the third or fourth century in Cologne with a number of companions, whose reported number "varies from five to eleven". Latin abbreviation for "Eleven martyr virgins" as "Eleven thousand virgins". From Wikipedia, the free encyclopedia. Redirected from 11th. This article is about the number. For other uses, see 11 disambiguation. This article has multiple issues. Please help improve it or discuss these issues on the talk page. Learn how and when to remove these template messages.

This article may contain indiscriminateexcessiveor irrelevant examples. Please improve the article by adding more descriptive text and removing less pertinent examples.

Devolver y volver a comprar rebajadoSee Wikipedia's guide to writing better articles for further suggestions. March Note that the digit zero 0 can not be in the number as integer division by zero is undefined.

Feel free to use analytics and clever algorithms to reduce the search space your example needs to visit, but it must do an actual search. Don't just feed it the answer and verify it is correct.

For maximum compatibility, this program uses only the basic instruction set. Ruling out 9- and 8-digit numbers see first paragraph in the Raku examplewe are looking for 7-digit numbers. The program does a brute force search, starting with the largest possible 7-digit number and iterates over all smaller numbers divisible by It checks for each iteration, if the number in question consists of different digits and is divisible by those digits.

In the hexadecimal case we cannot rule out digit numbers, thus all digits from 1 to f hex are present. The number has to be divisible by all its digits, therefore it has to be divisible by the least common multiple of the numbers 1, 2, 3, AWK does not support arbitrary long integers, so we have to use an array of digits for its representation.

It makes use of functions hexmod modulus and hexsub subtractionwhich act on an array. The program does a brute force search, starting with the largest possible digit number and iterates over all smaller numbers divisible by It checks for each iteration, if the number in question consists of different digits by construction it is then also divisible by its digits.

Harta cluj cu straziThe number can't contain 0 and 5, 0 is obvious, 5 because the number must end in 5 for it to be a multiple of that number and if that happens, all the even digits are ruled out which severely reduces the number's length since the other condition is that all digits must be unique. However, this means the number must be even and thus end only in 2,4,6,8. This speeds up the search by a factor of 2. The same approach when applied to hexadecimals takes a very long, long time.

This is a generic solution that works for any number base. The performance may be questionable for large bases which do not have a Lynch-Bell number using all digits. For a given subset, it finds the least common multiple for that subset and examines each multiple of the LCM which is between the largest and smallest positive numbers that can be constructed using each digit from that subset exactly once.

Upon finding many, it will simply select the largest element which is our answer. If there hadn't been any 7-digit solutions, it would have gone down to six and then five, etc. First member of a descending sequence of multiples of that uses the full set of 15 digits when expressed in hex.

The values foundall base 10 numbers that are divisible by their digits without repetitionare sorted descending, hence is the greatest number divisible by its digits in base Working in base 16 using the largest possible solution also a multiple of the least common multiple, subtract the LCM until all the digits appear. Descending from the upper limit, in steps of least common multiple of the fifteen digit valuesuntil the first number that uses all fifteen digits when expressed in hexadecimal.

The number can not have a zero in it, that implies that it can not have a 5 either since if it has a 5, it must be divisible by 5, but the only numbers divisible by 5 end in 5 or 0.

It can't be zero, and if it is odd, it can't be divisible by 2, 4, 6 or 8. So that leaves as possible digits the number can contain. The sum of those 8 digits is not divisible by three so the largest possible integer must use no more than 7 of them since 3, 6 and 9 would be eliminated.In most English-speaking countriesit is often written with a comma separating the thousands unit: 1, It may also be described as the short thousand in historical discussion of medieval contexts where it might be confused with the Germanic concept of the " long thousand " A period of 1, years is sometimes termed, after the Greek root, a chiliad.

A chiliad of other objects means 1, of them. From Wikipedia, the free encyclopedia. Redirected from number. For other uses, see disambiguation. Natural number. List of numbers — Integers. Mathematics portal. Retrieved October 25, OEIS Foundation. Retrieved Also star numbers".

Number Story: From Counting to Cryptography. New York: Copernicus. Also centered octagonal numbers". The Local. A court in Frankfurt Grossman Feb The American Mathematical Monthly.By using this site, you consent to the use of cookies.

You can refuse to use cookies by setting the necessary parameters in your browser. Math Fill in the largest unit digit to make them divisible by the numbers on the left.

Divisible by 4 2. Divisible by 8 3. Divisible by 11 4. Divisible by 12 5. Divisible by 11 Hepta is 7 sides, if they are all equal then mm is Other questions on the subject: Math. Jose can paint a house in 28 hours, his brother miguel, cab paint the same house Read More. Draw other squares of the same size and add the numbers on opposite cornerswhat Find the equation of the standard form of hyperbola foci 5,-2 and 5,10 the di Which of the following represent a linear inequality in open-sentence form?

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### Divisibility Rules and Tests

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**Divisibility Rules of 13 - Check if a number is a multiple of 13 (Divisible by 13)**

Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius! Real Life Math Skills Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

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Divisibility test calculator The following divisibility test calculator will help you to determine if any number is divisible by any other number.

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