Jackson forms a ten-digit number with distinct digits such that the first n number of digits form a number divisible by n, where n ranges from 1 to 10. Find the number.
Answers
Step-by-step explanation:
Since it is a 10 digit number, and the digits ar distinct, the digits in the numbers are 0, 1, 2, 3, 4, 5 ,6 , 7, 8, and 9
Taking advantage of the divisibility shortcut rules ...
Since the first n numbers is a number divisible by n ...
The 10 digit number is divisible by 10 ... so the last digiti is 0.
xxxxxxxxx0
The 5 digit number must be a number divisible by 5 ... so the 5th digit must be 0 0r 5. We have already used 0 and the digits are distinct. So the 5th digit is 5.
xxxx5xxxx0
The remaining even digits ... 2, 4 , 6, 8 ... must each reside in an even numbered slot ... 2, 4, 6. or 8
Also. the sum of the first 3 digits and the sum of the first 6 digits has to be a number divisible by 3 ... because both those numbers have to be divisible by 3
The 3rd and 4th digit must represent a number divisible by 4.
The sum of the first 9 digits must be a number divisible by 9
From here ... it is a trial and error process until you end up with a number that meets the criteria specified.
The answer is:
3816547290
CHECK:
3 ÷ 1 = 3
38 ÷ 2 = 19
381 ÷ 3 = 127
3816 ÷ 4 = 954
38165 ÷ 5 = 7633
381654 ÷ 6 = 63609
3816547 ÷ 7 = 545221
38165472 ÷ 8 = 4770684
381654729 ÷ 9 = 42406081
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3816547290 ÷ 10 = 381654729
Answer:
Answer is attached-
Step-by-step explanation:
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