# 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 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.

• Are there only two materials (iron and something else)? Aug 12 '17 at 9:12
• how do y check 3 set of 2 balls with the extra ball whle you can give max 2 balls to a person?
– Oray
Aug 12 '17 at 9:13
• @Oray We do it in three steps in some cases the single ball doesn't need to be checked consider we got $3$ "no"s checking the sets of balls then we can say the last one is from the majority. Aug 12 '17 at 10:23
• @JaapScherphuis No it can be only one or $4$ materials or others.But the point is that we know that at least four of them are from the same material. Aug 12 '17 at 10:24
• @TahaAkbari "divide the balls into 3 sets of two balls and a single ball the check that three sets of balls." what does this mean exactly? explain it with an real example please. It is confusing because you say "we can give two of them to a person" but if we can compare "a single ball" with "set of two balls", that's totally another story...
– Oray
Aug 12 '17 at 10:30