You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it’s the counterfeit. If they’re equal weight, the third coin is the counterfeit.
Brandon was walking around at the carnival. A man called out from a booth and said, “If I can write your exact weight on this piece of paper, you have to pay me $50. If I can’t do it, I’ll pay you $50.”
Brandon checked the booth for a scale but saw nothing. He agreed. Since your weight can fluctuate by a pound or two, he decided that no matter what number the man wrote, he would just say he weighed a pound more or less. In the end, the man in the booth won the $50. How did he do it?
From a basket of mangoes when counted in twos there was one extra, counted in threes there were two extra, counted in fours there were three extra, counted in fives there were four extra, counted in sixes there were five extra, but counted in sevens there were no extras.
At least how many mangoes were there in the basket?
119. The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can’t be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.
A man can make perfect counterfeit bills. They look exactly like real ones, they’re made of exactly the same materials, made the same way, everything. So perfect, one could pretty much call them real bills. One day he successfully makes a perfect copy of another bill. However, he gets caught when he tries to use the copy. How is this possible?
As a counterfeiter, he had lots of counterfeit bills around and he accidentally used one of them as his original. So he made a perfect copy of a counterfeit bill.