2020 AMC 10B Problems/Problem 15
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
Bash it out until you find a pattern. In the end, you'll see that the 
, 
, and the 
numbers are 
, giving the answer 
~DragonWarrior123
Solution 2
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 
~dolphin7
Video Solution
~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 | ||
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