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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2000 National Olympiad First Round
7
7
Part of
2000 National Olympiad First Round
Problems
(1)
Turkey NMO 2000 1st Round - P07 (Combinatorics)
Source:
7/24/2012
Some of
A
,
B
,
C
,
D
,
A,B,C,D,
A
,
B
,
C
,
D
,
and
E
E
E
are truth tellers, and the others are liars. Truth tellers always tell the truth. Liars always lie. We know
A
A
A
is a truth teller. According to below conversation,
B
:
B:
B
:
I'm a truth teller.
C
:
C:
C
:
D
D
D
is a truth teller.
D
:
D:
D
:
B
B
B
and
E
E
E
are not both truth tellers.
E
:
E:
E
:
A
A
A
and
B
B
B
are truth tellers.How many truth tellers are there?
<
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(
A
)
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1
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(
B
)
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2
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>
(
C
)
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3
<
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>
(
D
)
<
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>
4
<
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=
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>
(
E
)
<
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>
More information is needed
<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{More information is needed}
<
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>
(
A
)
<
/
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>
1
<
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>
(
B
)
<
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2
<
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>
(
C
)
<
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>
3
<
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c
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a
ss
=
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a
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x
−
b
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′
>
(
D
)
<
/
s
p
an
>
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
More information is needed