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4
2022 MMATHS Team Online p4 - even 3 digit numbrt in base b >=10
2022 MMATHS Team Online p4 - even 3 digit numbrt in base b >=10
Source:
October 1, 2023
number theory
MMATHS
Problem Statement
How many ways are there to choose three digits
A
,
B
,
C
A,B,C
A
,
B
,
C
with
1
≤
A
≤
9
1 \le A \le 9
1
≤
A
≤
9
and
0
≤
B
,
C
≤
9
0 \le B,C \le 9
0
≤
B
,
C
≤
9
such that
A
B
C
‾
b
\overline{ABC}_b
A
BC
b
is even for all choices of base
b
b
b
with
b
≥
10
b \ge 10
b
≥
10
?
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