MathDB
Problems
Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2014 Saudi Arabia Pre-TST
4.3
4.3
Part of
2014 Saudi Arabia Pre-TST
Problems
(1)
2013 pairwise different numbers game
Source: 2014 Saudi Arabia Pre-TST 4.3
9/13/2020
Fatima and Asma are playing the following game. First, Fatima chooses
2013
2013
2013
pairwise different numbers, called
a
1
,
a
2
,
.
.
.
,
a
2013
a_1, a_2, ..., a_{2013}
a
1
,
a
2
,
...
,
a
2013
. Then, Asma tries to know the value of each number
a
1
,
a
2
,
.
.
.
,
a
2013
a_1, a_2, ..., a_{2013}
a
1
,
a
2
,
...
,
a
2013
.. At each time, Asma chooses
1
≤
i
<
j
≤
2013
1 \le i < j \le 2013
1
≤
i
<
j
≤
2013
and asks Fatima ''What is the set
{
a
i
,
a
j
}
\{a_i,a_j\}
{
a
i
,
a
j
}
?'' (For example, if Asma asks what is the set
{
a
i
,
a
j
}
\{a_i,a_j\}
{
a
i
,
a
j
}
, and
a
1
=
17
a_1 = 17
a
1
=
17
and
a
2
=
13
a_2 = 13
a
2
=
13
, Fatima will answer
{
13.17
}
\{13. 17\}
{
13.17
}
). Find the least number of questions Asma needs to ask, to know the value of all the numbers
a
1
,
a
2
,
.
.
.
,
a
2013
a_1, a_2, ..., a_{2013}
a
1
,
a
2
,
...
,
a
2013
.
combinatorics