Help with a Math Problem, Please?

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1

<p>I listened to this problem from my friend over the phone, so the details might be a bit scratchy, but here is the crux of the problem:</p>

<p>There're 10 of each number from 0 to 9. How many combinations of <em>consecutive</em> numbers starting with 1 can be made?</p>

<p>a) 17
b) 18
c) 19
d) 22
e) 23</p>

<p>If there seems to be any impossible things about the question, please feel free to raise it, because it might likely de due to my poor hearing of the question itself from my friend. Thanks!</p>

2

<p>1,2
1,2,3
1,2,3,4
1,2,3,4,5
1,2,3,4,5,6
1,2,3,4,5,6,7
1,2,3,4,5,6,7,8
1,2,3,4,5,6,7,8,9</p>

<p>I would say eight but thats not a choice.</p>

3

<p>Nevermind, I found out the answer is 17, because the ten 1's can be used over and over again.</p>

<p>1
1,2
1,2,3
1,2,3,4
1,2,3,4,5
1,2,3,4,5,6
1,2,3,4,5,6,7
1,2,3,4,5,6,7,8
1,2,3,4,5,6,7,8,9
1,2,3,4,5,6,7,8,9,10
1,2,3,4,5,6,7,8,9,10,11
1,2,3,4,5,6,7,8,9,10,11,12
1,2,3,4,5,6,7,8,9,10,11,12,13
1,2,3,4,5,6,7,8,9,10,11,12,13,14
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17</p>

<p>Thank you, though, big<em>al</em>40. =) I had thought 8 at first, too, and proposed that to my friend, but she said it isn't amongst the given choices.</p>

4

<p>Actually if you look at it that way it would be 18.
1 is not a combination of consectuitve numberS
and you could also do 1-18 and 1-19</p>

5

<p>Big<em>Al</em>40:
Sorry, but I think Shina has it right at 17. The sequence 1,2,....,17 uses up all 10 instances of the digit '1' . There are no more available to use in the numbers '18' or '19' .</p>

6

<p>But it says there are 10 of each number...</p>

<p>NM I found out what you are saying like 1 second after posting.</p>

7

<p>Ahh. I agree with you opimizerdad, but that means the answer would be 16 unless 1 is considered a combination of consecutive numbers.</p>