Math Is Fun Forum

Where does it say that the two circles touch at only one point?  Or for that matter, even touch at all?

21. Take the number of your fingers multiplied by the number of you toes divided by one half and add it to the number of months in a year. What is the total?

22. A mother and father have six sons and each son has one sister. How many people are in that family?

23. Jenn has half the Beanie Babies that Mollie has. Allison has 3 times as many as Jenn. Together they have 72. How many Beanie Babies does each girl have?

24. Kevin is 14 inches taller than George. The difference between Kevin and Richard is two inches less than between Richard and George. Kevin at 6'6" is the tallest. How tall are Richard and George ?

25. A baseball team had just won the championship game and the players wanted to congratulate each other. They began shaking hands, but each player only shook hands with every other player just once. There are, of course, only 9 players on a baseball team. How many times did the players shake hands?

26. A jar has 4 amoebas in it to start. Amoebas split their cells in two ( therefore doubling in size) once every minute. The jar will be completely filled in 10 minutes. How long would it take to fill the same sized jar if had 8 amoebas in it to start?

27. There are 100 golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?

28. Two trains are on a head on collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound train is traveling at 80 miles per hour. What is the distance between the trains two minutes before they collide?

29. A car travels at a speed of 30 mph over a certain distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip?

30. A woman has 100 yards of cloth on a single roll, and she wants to divide it into 100 lengths of 1 yard each. It takes her 3 seconds to cut each length. Working non-stop, how long will it take her to cut all 100 pieces?

31. Find a simple method of solving:
6751X + 3249Y = 26751
3249X + 6751Y = 23249

32. Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How far does the pigeon travel?

33. Nick and John were exercising when the subject of weight came up. Nick had no problem telling John his weight, but John said he had more "mass" than he wanted. He wouldn't come right out and reveal his weight; so he told Nick this riddle. " I weigh 147 pounds plus half of my weight," he said. How much does he weigh?

34. A farmer knows that 20 of his hens, housed in 3 coops, will hatch 30 eggs in 18 days. How long will it take 30 hens, housed in 4 coops to hatch the same number of eggs?

35. How can you measure 1 gallon of juice out of a barrel, if all you have available is a 3-gallon and a 5-gallon pitcher?

36. Students at Monty High with a class size under of 30 took a math test. One third of the class got a "B", one quarter a "B-", one sixth a "C", and one eighth failed. The remainder of the students got an "A" How many students got an "A"?

37. When manufacturing bars of soap, the cutting machine produces scraps. The scraps from 11 bars of soap can be made into one extra bar. What is the total number of bars that can be made after cutting 250 bars of soap?

38. Kerry loves dumplings. He can eat 32 of them in an hour. His brother Pete needs 3 hours to eat the same amount. How long will it take them both together to eat 32 dumplings?

39. Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag?

40. Joan and Jane are sisters. Jean is Joan's daughter and 12 years younger than her aunt. Joan is twice as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?

LOL! Is it marked on your calendar?

"Random" has a meaning implied behind it which I think many have not heard of.

If I have 5 marbles in a bag, each a different color, and I have only a 10% chance of pulling out the blue marble, then the action of pulling out marbles is not a random one.

When we say random, we mean that the chances of all events happening are equal.

Now I believe statistically speaking, the number of digits in pi do not appear an equal number of times.  It's been a while, I'll have to see if I can find that again.  Thus, the digits in pi are not equal.

Now we only know a finite number of the digits.  So many this is only because we are looking at a subset of the digits that they aren't equal.  But when we've calculated it to over 50,000 places, thats normally enough to get a pretty good picture.

Here's a secret. It ain't that hard.

Apparently modern-day artillery pieces can do a very clever and powerful thing.

The scene: a corner of a desert; a large artillery piece, a few men and some vehicles.

The men load a shell, the piece is elevated and rotated, and then at a precise moment the shell is fired. The shell arcs into the sky, but the men continue working like clockwork. Another shell is loaded and the process is repeated. Again and again for a total of 9 times. The men then enter the vehicles and move on, to avoid a counterstrike.

At this point a viewer from above the planet would see each shell following its individual arc. Some high, some low, but more-or-less heading in the same direction.

Scene change: a group of tanks moving across the desert. The man in the lead tank yells "incoming", but they don't stand a chance. The desert erupts in 9 simultaneous explosions in a perfect 3x3 grid.

These three properties combine form what's called a group.  To restate them:

Identity exists: There exists an e in the group such that a + e = e + a = e for all elements a in the group.

Inverses exist: For all elements a in the group, there exists b in the group such that a + b = e.

Associativity: a + (b + c) = (a + b) + c for all elements a, b, c in the group.

Notice the letter e in the above.  "e" just stands for the identity.  So for example, for integers, e = 0.

Kurre, as luca pointed out, you make the assumption that pi's digits are random.  That does have to be the case.

For example, there doesn't have to be a 1/10th chance that the next digit will be 8.  There could be a 1/100th chance, and it would still be irrational.  Right now, we are finding that there are long strings of digits where 9 is completely absent.  We are trying to find out if at one point it will drop out all together.