Input : n = 200 Output : 199 If the given number is 200, the largest number which is smaller or equal to it having digits in non decreasing order is 199. Input : n = 139 Output : 139. Start from n, for every number check if its digits are in non decreasing order. If yes, then return. Else check for the next number until we find the result. Solution. Step1: Finding the largest and smallest 4-digit number without repetition of digits . We know that, . 9 >8 >7 >6 >5 >4> 3> 2> 1> 0. As we cannot use 0 as the first digit from left, . Thus, the smallest 4-digit number without repetition of any digit is 1,023. The greatest 4-digit number without repetition of any digit is 9,876. What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like. You can only use each digit once. For example: 34 x 2 = 68 or 3 + 4 2 = 19. First let’s calculate the largest five digit number, smallest 6 digit number is 100000, hence to find the largest five digit number, subtract 1 from the smallest 6 digit number. Hence, 100000 – 1 = 99999, which is the largest 5 digit number. Since, decimals and fractions are not included in the whole numbers, hence, 99999 is the largest 5 Examples : Input : n = 2 Output : 9009 9009 is the largest number which is product of two 2-digit numbers. 9009 = 91*99. Input : n = 3 Output : 906609. Below are steps to find the required number. Find a lower limit on n digit numbers. For example, for n = 2, lower_limit is 10. Find an upper limit on n digit numbers. Therefore, using given 4-digit numbers to form the greatest and smallest 3-digit number without repeating a digit. The numbers are 975 and 257. (ii) The given four-digit numbers are 6, 1, 4, 2 Now, we need to write the three-digit greatest and smallest number without repeating a digit on given four-digit numbers. Write all the 4-digit numbers that can be formed using 8, 6, 3, and 2 without repetition and count them. Also, find the smallest and the largest 4-digit number out of them. View Solution (a) In base six, the largest digit is 5. So, the largest four-digit number in base six would have all its digits as 5. Step 2/3 Therefore, the largest four-digit number in base six is 5555. (b) In base sixteen, the largest digit is F (which represents 15 in decimal). So, the largest five-digit number in base sixteen would have all its digits as Input : 313551 Output : 531135 Explanations : 531135 is the largest number which is a palindrome, 135531, 315513 and other numbers can also be formed but we need the highest of all of the palindromes. Input : 331 Output : 313 Input : 3444 Output : Palindrome cannot be formed. Naive Approach: The naive approach will be to try all the the probability that the first digit is 0,1,4, or 9 = 4/10. the probability that the second digit is one of the three not yet selected = 3/10. the probability that the third digit is one of the two not yet selected = 2/10. the probability that the final digit is the remaining one from the set of 0,1,4,9 = 1/10. i.e. ∏ i = 1 4 i 10. We already know the largest 4-digit number is 9999. We know that according to the division algorithm: Dividend = Divisor × Quotient + Remainder. Now once we divide 9999 by 16, we get: 9999 = 16 × 624 + 15. Now since 15 is the remainder when 9999 is divided by 16 it means that if we subtract 15 from 9999, we get a number perfectly divisible by The largest number of four digits exactly divisible by 77 is 01:14 What is the greatest three-digit number that can be formed from the digits $6,9,$ and $4 ?$ Use each digit only once. If any number N is divisible by a set of numbers a, b, c then the L.C.M. of a, b, and c also divides the number N. Calculation: The greatest 4 digit number is 9999. Arrange the digits 2, 6, 0, and 1 so that you create the highest possible four-digit number. So the way I like to think about it is, if I'm trying to create as large of a number as possible, I want to put the largest numbers in the largest place value. Hence the least number to be subtracted from =9999 so that it comes to be a multiple of 7 is 3. Hence the largest 4 digit number which is a multiple of 7 is 9999 − 3 = 9996 9999 − 3 = 9996. Hence option b b is correct. Note: If b = aq+ r where 0 ≤ r < a 0 ≤ r < a then the least non-negative number to be subtracted from b so that it 3Fryq5V.

4 digit largest number