Difference between revisions of "2003 AMC 12B Problems/Problem 8"
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==Solution== | ==Solution== | ||
− | Let <math>a</math> and <math>b</math> be the digits of <math>x</math>, | + | Let <math>a</math> and <math>b</math> be the digits of <math>\clubsuit(x)</math>, |
<cmath>\clubsuit(\clubsuit(x)) = a + b = 3</cmath> | <cmath>\clubsuit(\clubsuit(x)) = a + b = 3</cmath> |
Revision as of 18:31, 30 November 2019
- The following problem is from both the 2003 AMC 12B #8 and 2003 AMC 10B #13, so both problems redirect to this page.
Problem
Let denote the sum of the digits of the positive integer
. For example,
and
. For how many two-digit values of
is
?
Solution
Let and
be the digits of
,
Clearly can only be
or
and only
and
are possible to have two digits sum to.
If sums to
, there are 3 different solutions :
If sums to
, there are 7 different solutions:
The total number of solutions is
See Also
2003 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.