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India STEMS
2024 India STEMS
STEMS 2024 Math Cat A
P1
P1
Part of
STEMS 2024 Math Cat A
Problems
(1)
find all fancy pairs of (a,b)
Source: STEMS 2024, CAT A, P1
12/17/2023
Let
n
n
n
be a positive integer and
S
=
{
m
∣
2
n
≤
m
<
2
n
+
1
}
S = \{ m \mid 2^n \le m < 2^{n+1} \}
S
=
{
m
∣
2
n
≤
m
<
2
n
+
1
}
. We call a pair of non-negative integers
(
a
,
b
)
(a, b)
(
a
,
b
)
fancy if
a
+
b
a + b
a
+
b
is in
S
S
S
and is a palindrome in binary. Find the number of fancy pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
.
combinatorics