Difference between revisions of "2019 AMC 10C Problems/Problem 11"
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=== Solution === | === Solution === | ||
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| + | Since the number is in base 3, all the numbers are either 1 or 2. | ||
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| + | So, | ||
We could use casework: | We could use casework: | ||
Latest revision as of 16:16, 28 January 2020
Solution
Since the number is in base 3, all the numbers are either 1 or 2.
So,
We could use casework:
1 1 1 1 1 1 1 1 1 1 = 10 choose 0 = 1 case
1 1 1 1 1 1 1 1 2 = 9 choose 1 = 9 cases
1 1 1 1 1 1 2 2 = 8 choose 2 = 28 cases
1 1 1 1 2 2 2 = 7 choose 3 = 35 cases
1 1 2 2 2 2 = 6 choose 2 = 15 cases
2 2 2 2 2 = 5 choose 0 = 1 case
We add up 1 + 9 + 28 + 35 + 15 + 1 = 
cases.
~rg_ryse
