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2023 UMD Math Competition Part I
#16
Two identical digits
Two identical digits
Source: UMD 2023 I #16
October 23, 2023
UMD
algebra
Problem Statement
How many integers between
123
123
123
and
789
789
789
have at least two identical digits, when written in base
10
?
10?
10
?
a
.
180
b
.
184
c
.
186
d
.
189
e
.
191
\mathrm a. ~ 180\qquad \mathrm b.~184\qquad \mathrm c. ~186 \qquad \mathrm d. ~189 \qquad \mathrm e. ~191
a
.
180
b
.
184
c
.
186
d
.
189
e
.
191
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