My address is 1460 Sunset Boulevard.  First, you know that the house numbers are even and consecutive, so they must be approximately 1/6th the value of the sum (8790). In fact, the number that is 1/6th the total is the mean (average) for all 6 houses!  This number, 1465 (8790 / 6), is how you come to the conclusion.  There must be 3 house numbers greater than that number, and 3 house numbers less than that number, all being even and consecutive.

Therefore, the 6 house numbers are 1460, 1462, 1464, 1466, 1468, 1470.  The lowest house number, as per the question, is the answer: 1460.

Make the first two cuts as cross-sections, making 4 equal pieces.  The third and final cut is made horizontally through the middle, making a total of 8 pieces.

The man is 52 and his wife is 39.

The puzzle refers to the man as once being as old as the wife is “now.”  This gives you the first important piece of information; the man is older than the wife.  Second, you know that the two ages will add up to 91.  Third, you know that their difference in age is a constant variable.  You can’t, however, assume that they are close in age, but they must both be middle aged, otherwise it would be difficult to generate a number as high as 91 under the parameters of the problem.

So, after gathering this information, and some guess and check work, you’d find that the man is now twice the age (52) of her age (26) when he was the age she is now (39).

First, weigh all 12 marbles, 6 on each side of the scale (weighing #1).  Whichever side is heavier, take those 6 marbles and weigh 3 on each side (weighing #2).  Again, whichever side is heavier, take those 3 marbles, placing 1 to the side, and weighing the other 2, one on each side of the scale (weighing #3).  During this weighing, if one marble weighs heavier than the other, the answer is obvious, and so too, if they balance perfectly, then the marble you put to the side is the heavier marble!

The man first takes the chicken across, leaving it on the other side.  He returns alone in the canoe and picks up the bag of grain.  After bringing across the grain, he takes the chicken back to the original side, dropping him off, and picking up the fox.  After bringing the fox to the other side, and leaving it with the grain, the man returns back to the original side, retrieving the chicken, and making his 3rd and final trip crossing the river.  At no point was the fox left alone with the chicken, or the chicken with the grain.

Since Bill is Ken’s father-in-law, both Bill and Ken must be married.  This leaves the only remaining person, Mark, to be the bachelor (and hence the kicker).  Since Bill is taller than the receiver, Bill must not be the receiver.  By process of elimination, we conclude that Bill is the quarterback.  The remaining position (the receiver) goes to Ken.

Therefore, Bill is the quarterback, Ken is the receiver, and Mark is the kicker.

The black-haired child is a girl, and the red-haired child is a boy.

If at least one is lying, and there is one of each sex on the bench, then both must be lying.  If only one was lying, then there would be two children of the same sex.  Since the latter would not be following the given rules, then it is concluded that each child is of the opposite sex that they say they are.

The box that must be opened is the one labeled “apples and oranges.”  By definition, whichever fruit is inside, is the only fruit type that that box contains.  Let’s say that you found an apple in that box that was labeled with both apples and oranges; because you know it must therefore only contain apples, then you conclude that the box that is labeled “oranges” cannot contain only oranges, as all boxes have been said to be mislabeled.  Thus, the box labeled “oranges” must contain both apples and oranges, leaving the box labeled “apples” to contain only oranges.

Answer: Would your brother say that you tell the truth?

The key to this logic problem, is to find a question that the two brothers would answer differently, and that difference would therefore identify the two from each other.  The lying brother would answer the above question “yes.”  The truthful brother would answer the same question “no.”

F R U I T