Answer:
22098
Step-by-step explanation:
You want the difference between the largest and smallest 5-digit numbers whose digits are from the set {1, 2, 3} and include each of these at least once. The numbers cannot be divisible by 2 or 3.
The number will be divisible by 3 when its sum of digits is a multiple of 3. Since 1, 2, and 3 are prescribed digits, the remaining two digits must not have a total of 3 or 6. The largest possible remaining digits are {2, 3}, and the smallest remaining digits are {1, 1}. (Using {3, 3} for the largest digits would give a number divisible by 3.)
The number will be divisible by 2 if the least significant digit is 2. The largest and smallest digits are not 2, so that will not be an issue.
The largest number will place the largest available digit in the place with the highest place value: 33221.
The smallest number will place the smallest available digit in the place with the highest place value: 11123.
The desired difference is the difference of these numbers:
33221 -11123 = 22098 . . . . difference of largest and smallest
The difference between the two numbers will be 1998.
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
Given that Consider five-digit integers that have the following properties. Each of the digits is 1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not divisible by 2 nor divisible by 3.
The largest number will be 3211.
The smallest number will be 1213.
The difference between the largest and the smallest number will be calculated as,
D = 3211 - 1213
D = 1998
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