Weird Arrangements
In how many ways can be arranged such that the sum of any three consecutive integers is a multiple of 3.
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This is part of the set My Problems and THRILLER
The answer is 296.
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1 solution
Divide the given digits on the basis of wether they are of 3 k , 3 k + 1 , 3 k + 2 form.
If we place these forms consecutively in a fixed order throughout the 9 vacant places the condition would be fulfilled.
As 3 ∣ ( 3 k + 3 k + 1 + 3 k + 2 )
(Fixed order of forms can be k , k + 1 , k + 2 or k + 1 , k + 2 , k etc)
The order can be decided in 3 ! ways. Once the order is decided the no. Corresponding to a given form can be placed 3 ! ways. As each form has. 3 choices.
Finally total ways = 6 4 ways