Z is a three digit numbers such that all its digits are consecutive whole number(no zeros) with no repetition for example 867 and 765 are valid but 102 is not .how many of the Z are divisible by 12?
Answers
Given : Z is a three digit numbers such that all its digits are consecutive whole number(no zeros) with no repetition for example 867 and 765 are valid but 102 is not .
To Find : how many of the Z are divisible by 12
Solution:
three consecutive number
N -1 , N , N + 1 = 3N Divisible by 3
Hence to be divisible by 12 it must be divisible by 4 also
Number is divisible by 4 if last two digits are divisible by 4
04 , 08 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40 , 44 , 48 , 52 , 56 , 60 , 64 , 68 , 72 , 76 , 80 , 84 , 88 , 92 , 96
0 not used m repetition of digits not allowed
and maximum difference between digits = 2 N +1 - (N - 1) = 2
Hence only number satisfying these
12 , 24 , 32 , 56 , 64 , 68 , 76
312
324
456
756
564
768
576
876
There are 8 such possible numbers
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