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
Given : a ten-digit number with distinct digits such that the first n number of digits form a number divisible by n
n ranges from 1 to 10
To Find : Number
Solution:
Digits 0 to 9
Last digit has to be 10 as number Divisible by 10
5th Digit must be 5
2nd digit , 4th digit , 6th digit and 8th Digit must be even number
(2 , 4 , 6 , 8)
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 2468 2468 5 2468 2468 0
Sum of 1st three Digit must be divisible by 3
Sum of 1st 6 digit must be divisible by 3 as divisble by 6
Hence Sum of 4 to 6 Digit must be divisible by 3
while 5th Digit is 5
6 , 9 , 12 , 15 , 18 , 21
Sum of 4th & 6th Digit
= 1 , 4 , 7 , 10 , 13 , 16
4th digit , 6th digit are even
Hence only possible combination is 4 + 6 = 10
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 28 46 5 46 28 0
14 , 34 , 74 , 94 are not divisible by 4
while 16 , 36 ,76 , 96 are divisible by 4
Hence 4th Digit must be 6 hence 6th Digit must be 4
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 28 6 5 4 28 0
4 x (2,8) must be Divisible by 8
Digit for x available - 1 , 3 , 7 , 9
432 , 472 are divisible by 8
Hence 8th Digit must be 2 & 2nd digit must be 8
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 8 6 5 4 37 2 0
Sum of Digits 7 to 9 Divisible by 3
327 , 321 , 723 , 729 are possible
Sum of 1st 3 Digits is divisible by 3
183 , 381 , 189 , 981 , 789 , 987
possible numbers :
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 1 8 3 6 5 4 7 2 9 0
1836547 not divisible by 7
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 3 8 1 6 5 4 7 2 9 0
Satisfy all conditions :
3816547290
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 1 8 9 6 5 4 7 2 3 0
Digit 1 8 9 6 5 4 3 2 7 0
1896547 not divisible by 7
1896543 not divisible by 7
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 9 8 1 6 5 4 7 2 3 0
Digit 9 8 1 6 5 4 3 2 7 0
9816547 not divisible by 7
9816543 not divisible by 7
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 7 8 9 6 5 4 3 2 1 0
7896543 not divisible by 7
Digit position 1 2 3 4 5 6 7 8 9 10
Digit 9 8 7 6 5 4 3 2 1 0
9876543 not divisible by 7
3816547290 is 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.
3 /1 = 3
38/2 = 19
381/ = 127
3816/4 = 954
38165/6 = 7633
381654/6 = 63609
3816547/7 = 5,45,221
38165472/8 =47,70,684
381654729/9 = 4,24,06,081
3816547290/10 = 381654729
3816547290
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Answer:
3816547290
Step-by-step explanation:
It has to be a number of 10 digits and divisible by the digits, ranging from 1 to 10.