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Question Number 7165 by Tawakalitu. last updated on 15/Aug/16

30 teams participated in the football tournament . At the   end of the competition it turned out that in  Any group of three  teams it is possible to single out two  teams which score equal point in three games.   within this group (3 points are given for the victory,   1 point for the draw , 0 point for the defeat ).   what is the least possible number of draws that can occur  in such a tournament ?      please help me.  Please help .. thanks.

$$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\ $$$$ \\ $$$$ \\ $$$${please}\:{help}\:{me}. \\ $$$${Please}\:{help}\:..\:{thanks}. \\ $$

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