Ravi is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: “I lie on Monday and Tuesday.”

Day 2: “Today, it’s Thursday, Saturday, or Sunday.”

Day 3: “I lie on Wednesday and Friday.”

On which day does Ravi tell the truth**?**

**Solution**

*We know that Ravi tells the truth on only a single day of the week. If the statement on day 1 is untrue, this means that he tells the truth on Monday or Tuesday. If the statement on day 3 is untrue, this means that he tells the truth on Wednesday or Friday. Since Ravi tells the truth on only one day, these statements cannot both be untrue. So, exactly one of these statements must be true, and the statement on day 2 must be untrue.*

*Assume that the statement on day 1 is true. Then the statement on day 3 must be untrue, from which follows that Ravi tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would imply that the statement on day 2 is true, which is impossible. From this we can conclude that the statement on day 1 must be untrue.*

*This means that Ravi told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is a Sunday or a Monday. Because the statement on day 2 must be untrue, we can conclude that day 2 is a Monday.*

*So day 3 is a Tuesday. Therefore, the day on which Ravi tells the truth is Tuesday.*

**An explorer wishes to cross a barren desert**

An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?

**Solution**

*The answer is clearly that only two other men are required. The first helper only goes one day into the desert. He feeds the other two men during the first day, so that at the beginning of the second day, he only has one day rations left. So he goes back to camp. On the second day, the second helper feeds himself and the explorer. On the beginning of the third day the helper now has two days rations left so he heads back. The explorer is two days into the journey and still has all four days of his food left, so he continues on alone.*

**Pound of cotton or a Pound of gold**

Which would you say is heavier, a pound of cotton or a pound of gold?

**Solution**

*A pound of cotton is heavier than a pound of gold because cotton is weighted by the avoirdupois pound, which consists of 16 ounces, whereas gold, being a precious metal is weighted by the troy pound which consists 12 ounces. *

*(Generally we can say, one ounce of gold is heavier than one ounce of cotton and one pound of gold is lighter than one pound of cotton. )*