SOLUTION: Patty uses stickers with digits printed 0 to 9 to number the pages of her scrapbook. She has lots of all digits except the digit 3, and she only has 37 of these. How many pages can

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Question 1132049: Patty uses stickers with digits printed 0 to 9 to number the pages of her scrapbook. She has lots of all digits except the digit 3, and she only has 37 of these. How many pages can she number in her scrapbook with this limitation?
Found 3 solutions by Alan3354, josmiceli, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Patty uses stickers with digits printed 0 to 9 to number the pages of her scrapbook. She has lots of all digits except the digit 3, and she only has 37 of these. How many pages can she number in her scrapbook with this limitation?
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I don't think there's an algebraic solution or a formula for this.
It's a matter of listing the numbers and counting the 3's.
You can do that as well as anyone else.
I'll be glad to check your answer if you send it via the TY note.
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Copied from josmicelli:
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She will use up:
numbers with 3. number of threes
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3 - - - - - - - - - - - - 1
13 - - - - - - - - - - - - 1
23 - - - - - - - - - - - - 1
30 - 33 - 39 - - - - - - 11
43 - - - - - - - - - - - - 1
53, 63, 73, 83, 93 - - - 5
103, 113, 123, - - - - - - 3
130, 131, 132 - - - - - - 3
133 - - - - - - - - - - - - 2
134 - 139 - - - - - - - - 6
143, 153, 163, - - - - - - 3
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total of 3's used = 37
She can number pages up to page 163
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She can add pages 164 to 172, 9 more pages.
---> 172 pages.
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Another example where I would have had the student figure it out.
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Are we helping them by giving them the answers?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
She will use up:
numbers with 3. number of threes
---------------- -------------------
3 - - - - - - - - - - - - 1
13 - - - - - - - - - - - - 1
23 - - - - - - - - - - - - 1
30 - 33 - 39 - - - - - - 11
43 - - - - - - - - - - - - 1
53, 63, 73, 83, 93 - - - 5
103, 113, 123, - - - - - - 3
130, 131, 132 - - - - - - 3
133 - - - - - - - - - - - - 2
134 - 139 - - - - - - - - 6
143, 153, 163, - - - - - - 3
-------------------------------
total of 3's used = 37
She can number pages up to page 163

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
lets group the numbers into groups of 0-9, 10-19, 20-29, 30-39, 40-49 ...
in group 0-9+there is only 1 three used:
10-19 there is only 1three used :
20-29 there is only 1 three used:
30-39 there are 11 three used :
40-49 there is only 1 three used :
50-59 there is only 1 three used:
60-69 there is only 1 three used:
70-79 there is only 1 three used:
80-89 there is only 1 three used:
90-99 there is only 1 three used
=>There are a total of 20 threes used from 1-99 pages.
now we are only have 17 threes left, so count 17 threes from each group and you will get to number 163.
At number 163, all the threes are used. after 163, numbers 164-172 do not use the number three again so the number of pages she can do total is 172+pages with no leftovers of threes.