Answers for the last five questions below.
Due to the high number of messages, may I ask that you post direct. What the hell, it's only a bit of fun. Right or wrong, I will always post a full answer.
Q. You drive to the store at 20 mph and return by the same route at 30 mph. discounting the time spent at the store, what was your average speed?
A. Let d be the distance to the store, T be the time it gets to get there, t be the time it takes to get back, and A be the average speed (which is what we want to find out). As we know from elementary mathematics, distance equals rate times time:
d = 20T
T = d/20
d = 30t
t = d/30
Now that we have expressions for T and t, we can come up with an equation that describes the round trip:
2d = A(T + t)
2d = A(d/20 + d/30)
2d = A(3d/60 + 2d/60)
2d = A(5d/60)
A = 120d/5d
A = 24
So the average speed is 24 mph. If this seems strange to you, consider that more time is spent traveling at 20 mph than time spent at 30 mph, so the "20 mph" figure should count more toward the average.
Q. A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time elapsed between the first and second observations?
A. The hour hand is exactly on a minute mark five times per hour -- on the hour, twelve minutes past the hour, twenty four minutes past, thirty six minutes past, and forty eight minutes past.
Let X be the number of hours, and Y be the number of minutes past the hour. When the hour hand is on a minute mark, the position of the hour hand is 5X + Y/12, and the position of the minute hand is Y. On the first occasion, Y = 5X + Y/12 + 6. This is equivalent to 60X = 11Y - 72. Since Y can only take one of the values in the set { 0, 12, 24, 36, 48 }, it can be determined that the only legal values for the equation are X = 1 and Y = 12. So the time is 1:12.
Similarly, the second occasion's equation is 60X = 11Y - 84. The only legal values here are X = 3 and Y = 24. So the time is 3:24.
Between 1:12 and 3:24, two hours and twelve minutes have elapsed.
Q. On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?
Solution #1
Let x be the age of the man at the time of his death. His age consists of the number of years he spent as a child plus the number of years he spent as a teenager plus the number of years between his coming of age and his marriage plus five plus his son's age (half his own) plus four. In mathematical terms, this is:
x = x/6 + x/12 + x/7 + 5 + x/2 + 4
x = 14x/84 + 7x/84 + 12x/84 + 42x/84 + 9
x = 75x/84 + 9
84x/84 - 75x/84 = 9
9x/84 = 9
x/84 = 1
x = 84
So the man lived to be 84 years old.
Solution #2
The man lived 1/12 of his life as a teenager. There are seven teen years. 7 x 12 = 84.
Q. Missing Link
A. Won't that smarmy concierge be impressed when you make all the exchanges with only one cut?
The cut must be made in a link which is third from the end (either end, it doesn't matter). This one cut allows this link to detach itself from a set of two links, and a set of four links. There, now you have one, two, and four links.
On day one the concierge is given the cut link. On day two, he returns the cut link in exchange for the two joined links. On day three you give him the cut link again. On day four, he returns all links and is given the set of four. On day five you give him the cut link. On day six you exchange the two links for the one. On day seven he has all the links- and then western union arrives in the nick of time.
Q. What is the name of this classic?
A. The classic is "Little Red Riding Hood". To translate, simply read the passage aloud. Each word is phonetically very similar to the words of the actual story. The narrative was composed in 1940 by a professor named H. L. Chace.
I think it fair to say Frank has his nose ahead at this time, but, to be seen to be fair The following is the tie-break. First correct post wins.
There were once three men who were in competition for the hand of a young woman. Therefore, they decided to have a three-person duel to see which of them would marry her. Wait, that is not right- it was two men and the woman's father. On the other hand, was it three brothers competing for their father's fortune?
No, I remember now, they were duelling to see which of them was the greatest Puzzler of all time. Yes, that was it. I forgot their names, so we will call them Alex, Bob, and Chris. Alex was an expert swordsman, which was really too bad, since by tradition this was going to be a pistol duel. As a pistol shot, he was third-rate. Alex hits his target only 30% of the time. Chris was quite a bit better, hitting his target 50% of the time. Bob was the best of all, never missing a shot.
To compensate for the obvious inequities in their marksmanship skills, they would fire in turns, beginning with Alex, followed by Bob and then Chris. The cycle would repeat until there was but one man standing (with breaks to reload if necessary).
I don't recall the outcome of the duel, but assuming each knew the others' ability and used the optimum strategy, which had the best chance of surviving, and what were his odds?
That man would be remembered as, the ?'Greatest Puzzler of All Time'.
(Or, at least until the end of the week) :wink:
For the first time ever, a puzzle which, you only THINK the answer. Strange but true.
In an effort to prove I can read minds and to confound the sceptics amongst you, I propose an experiment.
Think of a country beginning with the letter ?'D'
Take the last letter of this name, and think of an animal.
Take the last letter of this name, and think of a color.
Don't post what they are. Within 24 hours I will be able to tell you!
