The smallest one allowable is 331.

All must begin with 3,4,5, or 6.  However, finding how many begin
with 3 is different from finding how many are langer.  Also, of those
beginning with 3, finding how many begin with 33 is different from 
finding how many begin with 34, 35, or 36.

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First we count all the three digit numbers beginning with 33:

We can choose only 1, 2, 3, 4, 5, or 6 for the third digit.  That's 6
choices for the third digit of those beginning with 33.

So there are 6 allowable 3-digit numbers beginning with 33.  These are

331, 332, 333, 334, 335, or 336.

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Next we must find how many begin with 34, 35, or 36.

We can choose the second digit any of 3 ways (either 4, 5 or 6)

We can then choose the third digit any of the total 7 ways.

That's 3x7 or 21 allowable 3-digit numbers beginning with 34, 35, or 36

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Finally we must find how many 3-digit numbers beginning with 4, 5, or 6

We can choose the first digit any of 3 ways (4, 5, or 6)

We can choose the second digit any of the 7 ways.

We can choose the third digit and of the 7 ways.

That's 3x7x7 or 147 allowable 3-digit numbers beginning with 4,5, or 6

Answer: 6 + 21 + 147 = 174

Edwin