Talk About Limbo

You are in LImbo. The administrator challenges you to a game. He will think of a natural number, and you can have one guess at it each day. (Once he has thought of his number, he will never change it.) If you guess it, he'll let you out. Will you get out? (Remember - you have eternity...) Explain.

What if he instead told you that he was going to pick an integer - now will you get out? What about if he chose a rational number? A real number?

Make 24

Using the numbers 3, 3, 8, and 8, and the four basic operations +,-,/,* make 24.

Good Old Fashioned Banking

John needed some small bills because he was traveling. He went into a bank and gave the teller a $100 bill. He told her, "I need some two-dollar bills, ten times as many one-dollar bills, and the rest in five-dollar bills. Assuming she didn't tell him to try his request online instead, how many of each did the teller give him?

3 Bags of Marbles

You have three bags, each containing two marbles. Bag #1 contains two white marbles, bag #2 contains two black marbles, and bag #3 contains one white marble and one black marble.

You pick a random bag and take out one marble. Given that this is a white marble, what is the probability that the remaining marble from the same bag is also white?

Up to 100

Use the numbers 123456789 so that the equation is equal to 100. The numbers must stay in the same order. You can use addition, subtraction, multiplication, and division. Remember, they have to stay in the same order.

Been A While Since I Did Some Statistics

How many 2 digit numbers can you make using the digits 1, 2, 3 and 4 without repeating the digits?

Prime Time Soccer

At the end of the soccer season, every player had scored a prime number of goals and the average for the eleven was also a prime number.  No player's tally was the same as anyone else's, and neither was it the same as the average.

Given that nobody had scored more than forty-five goals, how many goals did each player score?

Like yesterday, this puzzle comes out of The World's Biggest Book of Brainteasers & Logic Puzzles.

Is it Possible

Find a 5 digit number, as big as possible, that when you multiply it by a single digit number, you get a six digit number, in which all digits are identical.

Three Darts in One Hemisphere

You throw three darts onto the surface of a globe, each from a randomly chosen direction. What is the probability that all three darts are in one hemisphere?

Six Digits

You have a number that consists of 6 different digits. This number multiplied by 2, 3, 4, 5, and 6 yields, in all cases, a new 6-digit number, which, in all cases, is a permutation of the original 6 different digits. What's the number?

Create Twenty-Four

Create the number 24 using (all of) 1, 3, 4, and 6. You may add, subtract, multiply, and divide. Parentheses are free. You must use each digit only once. Note that you may not "glue" digits together. (14 - 6) * 3 is not a solution. 13 * 4 * 6 is not a solution either (powers not allowed).

A Counting Problem

How many terms are contained in (a + b + c)²⁰ .

Moon Cable

A large space agency has decided to build a base on the moon. For this purpose, a cable must be laid around the moon's equator. When the cable is laid, it turns out to be 1 meter short. In a quickly arranged meeting, it is decided to investigate the possibility to lay the whole cable in a groove.

How deep does the groove need to be to make this work?

The agency's director considers digging a groove, no matter how deep, around the entire circumference is too expensive. He suggests to lay the whole cable just a bit north of the equator. How many meters north of the moon's equator should the cable be laid to settle the problem of the lacking 1 meter of cable?

Random Walk

A drunk leaves a bar (rather forcefully).  After standing up and dusting himself off (rather unsuccessfully), he decides to walk home.  Unfortunately for him, he has no idea where home is and has no way of deciding which way to go.  He is on a street traveling east-west only, making things simpler for him.

With each step, he's just as likely to turn around and walk back in the direction he came from.  After 20 steps, how likely is it he will be back where he started from (right in front of the bar)?

Split the Tab

You've been out to a restaurant with a group of people from work. The bill is now on it's way. Time for either a bit of philosophy/game theory. What's the best way to handle the bill? You have three choices: Split the bill evenly, pay for what you ordered, or got to the trouble of asking for separate checks?

For a good write up on the problem, try mindyourdecisions.

Not Exactly Chicken Nuggets

On a nice summer day, two tourists visit the Dutch city of Gouda. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot bitterballs. The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20.

What is the largest number of bitterballs that cannot be ordered in these portions?

How Good Are You at Adding

   ABCABA
   BBDCAA
   ABEABB
+ ABDBAA
--------------
AAFGBDH

Each letter represents one digit.  No two letters represent the same digit.

What's the sum equal to?

Packing Socks in the Dark

Image via Wikipedia

In your bedroom you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. The socks are all jumbled together in the drawer. It is dark in your bedroom, your partner is still asleep and so you don't want to turn on the light to see. So you cannot see which sock is which in the dark.

You are packing for a trip that will take you three days, so you need three pairs of socks.

How many socks do you need to take out to be sure that you have at least three pairs of socks of the same color?

Make Just One Move

26 - 63 = 1

The above equation is wrong, but can you fix it with just one move?

Anyone Else Back From Vacation?

Image via Wikipedia

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly

How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?