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Cono Sur Olympiad
2008 Cono Sur Olympiad
3
3
Part of
2008 Cono Sur Olympiad
Problems
(1)
Two friends must guess the other's number
Source: Cono Sur 2008 #3
11/17/2015
Two friends
A
A
A
and
B
B
B
must solve the following puzzle. Each of them receives a number from the set
{
1
,
2
,
…
,
250
}
\{1,2,…,250\}
{
1
,
2
,
…
,
250
}
, but they don’t see the number that the other received. The objective of each friend is to discover the other friend’s number. The procedure is as follows: each friend, by turns, announces various not necessarily distinct positive integers: first
A
A
A
says a number, then
B
B
B
says one,
A
A
A
says a number again, etc., in such a way that the sum of all the numbers said is
20
20
20
. Demonstrate that there exists a strategy that
A
A
A
and
B
B
B
have previously agreed on such that they can reach the objective, no matter which number each one received at the beginning of the puzzle.
combinatorics
cono sur