This is Mathness!
You are given digits from to .A crazy set is a set whose elements are one or more numbers whose digits are taken from to ,each digit used once compulsorily(in the whole set).
[For example ,
is crazy set because it consists of all digits
and in the total set each digit is used once!! Similarly
is also a crazy set.]
Find the number of crazy sets whose sum of elements is 100 .
The answer is 0.
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Clearly for the sum to be 100 we cannot have any 3 digit numbers.....and since each digit is used once only,the sum of the digits of all the numbers will be 1 + 2 + . . . + 9 = 4 5 ..Let the sum of the numbers in the tens digit be x ..So the sum of the number of the unit's digit = 4 5 − x ...Hence the value of the total number = 1 0 ∗ x + 4 5 − x = 4 5 + 9 x Clearly 100 is not of the form 4 5 + 9 x ..Hence it is not possible.....