MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2019 India IMO Training Camp
2019 India IMO Training Camp
Part of
India IMO Training Camp
Subcontests
(4)
3
1
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Coins on a table
There are
2019
2019
2019
coins on a table. Some are placed with head up and others tail up. A group of
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2019
persons perform the following operations: the first person chooses any one coin and then turns it over, the second person choses any two coins and turns them over and so on and the
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-th person turns over all the coins. Prove that no matter which sides the coins are up initially, the
2019
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persons can come up with a procedure for turning the coins such that all the coins have smae side up at the end of the operations.
P3
1
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NT disguised as Algebra
Let
n
≥
2
n\ge 2
n
≥
2
be an integer. Solve in reals:
∣
a
1
−
a
2
∣
=
2
∣
a
2
−
a
3
∣
=
3
∣
a
3
−
a
4
∣
=
⋯
=
n
∣
a
n
−
a
1
∣
.
|a_1-a_2|=2|a_2-a_3|=3|a_3-a_4|=\cdots=n|a_n-a_1|.
∣
a
1
−
a
2
∣
=
2∣
a
2
−
a
3
∣
=
3∣
a
3
−
a
4
∣
=
⋯
=
n
∣
a
n
−
a
1
∣.
P2
5
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P1
4
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