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Jaap Scherphuis
Jaap Scherphuis
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We have $7$ balls that at least $4$ of them are made from iron.In In a step we can give two of them to a person that can recognize whether oror not the balls are made from the same materials. How many movessteps are at least needed to find a ball that is from the majoritymade of iron?

My attempt:It It is easy to see $4$ movessteps are enough it. All that is just needed is to divide the balls into $3$ sets of two balls and a single ball the, then check thatthose three sets of balls.Then Then we have to divide the cases according to the number of "Yes" or "No"'s that we hear.Finally you can get Finally, in some of those cases the three issteps were enough, and in some a $4$th step is enoughneeded.But But I can't prove $3$ steps can't be enough.

We have $7$ balls that at least $4$ of them are made from iron.In a step we can give two of them to a person that can recognize whether or not the balls are made from the same materials. How many moves are at least needed to find a ball that is from the majority?

My attempt:It is easy to see $4$ moves are enough it is just needed to divide the balls into $3$ sets of two balls and a single ball the check that three sets of balls.Then we have to divide the cases according to the number of "Yes" or "No"'s that we hear.Finally you can get in some cases three is enough and in some $4$ is enough.But I can't prove $3$ steps can't be enough.

We have $7$ balls that at least $4$ of them are made from iron. In a step we can give two of them to a person that can recognize whether or not the balls are made from the same materials. How many steps are at least needed to find a ball that is made of iron?

My attempt: It is easy to see $4$ steps are enough. All that is needed is to divide the balls into $3$ sets of two balls and a single ball, then check those three sets of balls. Then we have to divide the cases according to the number of "Yes" or "No"'s that we hear. Finally, in some of those cases the three steps were enough, and in some a $4$th step is needed. But I can't prove $3$ steps can't be enough.

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Taha Akbari
Taha Akbari
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How many moves are at least needed to find a ball that is from the majority?

We have $7$ balls that at least $4$ of them are made from iron.In a step we can give two of them to a person that can recognize whether or not the balls are made from the same materials. How many moves are at least needed to find a ball that is from the majority?

My attempt:It is easy to see $4$ moves are enough it is just needed to divide the balls into $3$ sets of two balls and a single ball the check that three sets of balls.Then we have to divide the cases according to the number of "Yes" or "No"'s that we hear.Finally you can get in some cases three is enough and in some $4$ is enough.But I can't prove $3$ steps can't be enough.