My Fussy Number

How many three-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9 which are divisible by 5, greater than 500, and none of the digits is repeated?


The answer is 12.

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2 solutions

展豪 張
Apr 19, 2016

As the required number is divisible by 5, the digit place must be 5.
As it is greater than 500, the hundred place is 6, 7 or 9 (5 is already used).
Ten place can be chosen among the remaining four digits.
Answer = 1 × 3 × 4 = 12 =1\times 3\times 4=12


Paola Ramírez
Apr 19, 2016

As the number has to be divisible by 5 5 , its last digit is 5 5 . Then, the hundreds digit could be 6 , 7 6,7 or 9 9 , and the tens digit could be any of the six numbers without counting the hundreds digit either 5 5 .

It can be formed 3 × 4 × 1 = 12 numbers 3\times 4\times 1=\boxed{12 \text{ numbers}}

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