IMO Shortlist 2002 problem C4
Kvaliteta:
Avg: 0,0Težina:
Avg: 7,0 Let
be the set of ordered triples
, where
are integers with
. Players
and
play the following guessing game. Player
chooses a triple
in
, and Player
has to discover
's triple in as few moves as possible. A move consists of the following:
gives
a triple
in
, and
replies by giving
the number
. Find the minimum number of moves that
needs to be sure of determining
's triple.
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
![(x,y,z)](/media/m/5/2/e/52e5ec762ff5263770c6e6c12cb9838e.png)
![x,y,z](/media/m/b/7/2/b72c022e9d438802d328d34eb61bb4ba.png)
![0\leq x,y,z\leq9](/media/m/0/2/2/022f0dee8a68d35d90f87a6c98083e6f.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![(x,y,z)](/media/m/5/2/e/52e5ec762ff5263770c6e6c12cb9838e.png)
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![(a,b,c)](/media/m/0/c/2/0c2cda0a5087208400fdd3678b9d97e1.png)
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![\left|x+y-a-b\right |+\left|y+z-b-c\right|+\left|z+x-c-a\right|](/media/m/8/f/3/8f3b1e391c42949ef6e1ef75ba65b6fe.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2002