Difference between revisions of "2020 AMC 10B Problems/Problem 15"
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Revision as of 00:18, 9 July 2020
Contents
Problem
Steve wrote the digits ,
,
,
, and
in order repeatedly from left to right, forming a list of
digits, beginning
He then erased every third digit from his list (that is, the
rd,
th,
th,
digits from the left), then erased every fourth digit from the resulting list (that is, the
th,
th,
th,
digits from the left in what remained), and then erased every fifth digit from what remained at that point. What is the sum of the three digits that were then in the positions
?
Solution 1
After erasing every third digit, the list becomes repeated. After erasing every fourth digit from this list, the list becomes
repeated. Finally, after erasing every fifth digit from this list, the list becomes
repeated. Since this list repeats every
digits and since
are
respectively in
we have that the
th,
th, and
st digits are the
rd,
th, and
th digits respectively. It follows that the answer is
Video Solution
https://youtu.be/t6yjfKXpwDs ~IceMatrix
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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.