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.
A slight inclination of the cranium is as adequate as a spasmodic movement of one optic to an equine quadruped utterly devoid of any visionary capacity.
Translate this rather strange sentence into one that is more sensible.
If a cork is placed into a glass of water, it will almost always drift to the side of the glass. There is one simple way, however, to get the cork to float in the center of the glass. What is it?
Water, the glass, and the cork are all that is required.
The reason that a cork drifts to the side of a glass is that it floats to the highest point. Since water “clings” to the glass, the highest point is around the edge of the water. To get the cork to float in the middle of the glass, all you have to do is fill the glass as much as possible. The water will form a convex shape above the glass, with the highest point at its center. This is where the cork will settle.
A couple has two children. At least one of them is a boy. Assuming the probability of having a boy or girl is 50%, what is the probability that both children are boys?
If you answered 1/2, you’re not without comrades, but the generally accepted answer by statisticians (though not without debate) is 1/3. This is because there are four possible combinations: boy-boy, boy-girl, girl-boy and girl-girl. Since we are told one of the children is a boy (but we don’t know if it’s the first or second child), we can rule out the girl-girl combination, leaving three remaining options. Only one out of 3 is boy-boy, so we get a 1/3 chance.
She will always need to give you 5 apples. You both need at least 5 apples to begin with, but apart from that it doesn’t matter exactly how many you each have. When she gives you 5 you will have 10 more than her because she will lose 5 and you will gain 5, resulting in a net difference of 10.
For example, if you each have 25 apples and she gives you 5 of hers, she will be left with 20 and you will now have 30, precisely 10 more than she has.