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2020 Princeton University Math Competition
6
6
Part of
2020 Princeton University Math Competition
Problems
(1)
2020 PUMaC Team 6
Source:
1/1/2022
We say that a string of digits from
0
0
0
to
9
9
9
is valid if the following conditions hold: First, for
2
≤
k
≤
4
2 \le k \le 4
2
≤
k
≤
4
, no consecutive run of
k
k
k
digits sums to a multiple of
10
10
10
. Second, between any two
0
0
0
s, there are at least
3
3
3
other digits. Find the last four digits of the number of valid strings of length
2020
2020
2020
.
number theory