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Bangladesh Mathematical Olympiad
2022 Bangladesh Mathematical Olympiad
4
4
Part of
2022 Bangladesh Mathematical Olympiad
Problems
(1)
Easy combinatorics about finding minimum integer
Source: BdMO 2022 Secondary P4
4/12/2022
Pratyya and Payel have a number each,
n
n
n
and
m
m
m
respectively, where
n
>
m
.
n>m.
n
>
m
.
Everyday, Pratyya multiplies his number by
2
2
2
and then subtracts
2
2
2
from it, and Payel multiplies his number by
2
2
2
and then add
2
2
2
to it. In other words, on the first day their numbers will be
(
2
n
−
2
)
(2n-2)
(
2
n
−
2
)
and
(
2
m
+
2
)
(2m+2)
(
2
m
+
2
)
respectively. Find minimum integer
x
x
x
with proof such that if
n
−
m
≥
x
,
n-m\geq x,
n
−
m
≥
x
,
then Pratyya's number will be larger than Payel's number everyday.
combinatorics