Følgene strategi er bra for brødrene flip. Begge roper 1 hvis de har 6er på den første plassen, og 2 hvis det ikke er 6er på første plass. Noter at sjansen på at begge roper 1 er 1/36, og at sjansen for at de begge har 6 på plass 2 og ikke 6er på plass 1 er større enn 0. Denne strategien vil derfor...

New problem: Big Flip and Lil Flip play the following game. First each of them independently roll a dice $100$ times in a row to construct a $100$-digit number with digits $1,2,3,4,5,6$ then they simultaneously shout a number from $1$ to $100$ and write down the corresponding digit to the number oth...

I must say that I'm thoroughly disappointed by the prevalent use of Norwegian in this forum (considering many of its members must practice writing proofs in English for international contests)! Especially the use of terminology such as "omorganisering" for "permutation" makes me ...

New problem: Let $ABCD$ be a cyclic quadrilateral. Point $P$ is on line $CB$ such that $CP=CA$and $B$ lies between $C$ and $P$. Point $Q$ is on line $CD$ such that $CQ=CA$ and $D$ lies between $C$ and $Q$. Prove that the incentre of triangle $ABD$ lies on line $PQ.$

Sorry for poor formatting, am on mobile. We use induction on number of digits, and we will prove that one can find an $n$ digit number consisting of only $2$s and $5$s that is divisible by $2^n$. For $n=1$ it's trivial, as $2$ is divisible by $2^1$. Inductive step: Assume we have an n digit number c...