Altogether there are 42 bags of jellybeans and 41 jellybeans in each bag. What is the probability that the first three jellybeans a guest randomly removes from her bag are the same flavor?

Check Braingle.com for the answer. ]]>

(To rotate the number left, take the first digit off the front and append it to the end of the number. 2591 rotated to the left is 5912.)

Check Braingle.com for the answer. ]]>

How many natural numbers less than a googol are both the square of a square and the cube of a cube?

(If N is an integer then N^2 is a square and N^3 is a cube.)

Check Braingle.com for the answer. ]]>

The island has a strange courtship custom. Before a father will give permission for his daughter to marry, her suitor must bring the father a fish each day until he has traveled by every route from his village to the father's village. The young man only travels along routes where he is always getting closer to his destination. The young man may visit other villages along the way.

On April first a father's three sons come to tell him of their intent to woe a bride, each from a different village. The brides' villages are the first three villages encountered when traveling clockwise around the island.

If the sons begin their courtship today and the couples are married on the day following each son's last trip, what are the three wedding dates?

Bonus Question: If the coastline of the island is ten miles long, how long is the longest route that any of the sons takes to reach their betrothed's village?

Check Braingle.com for the answer. ]]>

On their turn each player may either pass or double the antes for all the players. After the third player's turn all the dice are revealed to determine the winner.

The winner is the person with the most dice with the same value. If two or more players have the same number of matching dice, then the higher value of the dice wins. For example, four ones beat three sixes, but three sixes beat three fives. If two or more players have the same number and value for the winning roll, then they split the antes. The starting person rotates so that the person who went first in a round goes last in the next round.

On the first round you roll a pair of sixes. Harry passed on his turn and now it's your turn. You know that Harry would have doubled the ante if he had three of a kind or better, but that he wouldn't double the ante with a pair when having to go first. So Harry could have the same roll as you, but you're not worried about Harry beating you. You also know that Tom will also double the ante on his turn if he has three of a kind or better, but that he won't double it with a pair.

Should you pass or double the antes?

Bonus question: Does your action change if instead of splitting the antes on a tie, the antes instead stay in the pot for the next round?

Check Braingle.com for the answer. ]]>

"All of the digits are different. The digital sum matches the number formed by the last two digits in the number. The sum of the first two digits is the same as the sum of the last two digits."

"Take the sum of the number, the number rotated one to the left, the number rotated one to the right, the number with the first three and last three digits swapped, the number with the digit pairs rotated to the left, and the number with the digit pairs rotated to the right. The first and last digits of this sum match the last two digits of the number, in some order."

Ralph then asks, "If each of the three numbers formed by the digit pairs in the number is prime, then what is the number?"

Rex looks confused, and for a moment Ralph thinks he's finally gotten him. Then Rex smiles, scribbles a few things down on a pad of paper and then says, "Very nice, Ralph!"

Rex then tells Ralph his number.

What did Rex say?

(See the hint for an explanation of the terminology.)

Check Braingle.com for the answer. ]]>

Is a ball more likely to hit the hoop or go through the hoop without hitting it?

Bonus question: What size hoop would you need in order to have the probability of a ball going through the hoop without hitting it equal the probability of hitting the hoop?

Check Braingle.com for the answer. ]]>

He tells Rex, "The lot my house sits on is a regular polygon. My house is a matching regular polygon sitting on a circular foundation in the middle of the yard. The closest part of the foundation to the edge of my property is exactly the same as the diameter of the foundation. The house is two stories, built around a central circular atrium with a diameter that is exactly one tenth the longest measurement of my property."

"Sounds like quite the house!" remarked Rex.

"Yes, I've been building it for almost two years. When I was excavating the foundation I found a section of an old irrigation pipe. The pipe exactly bisected the area of the house, with each end of the pipe at an edge of the house. After the house was completed while I was preparing to put up a fence around the edge of the property, I discovered that the length of the pipe I found was exactly the length of one side of the property. I used the pipe as a gate across the side of the property with the driveway and built the fence around the other sides. I built a total of 400 feet of fence."

"So what's the square footage of my house?" Ralph asked.

"Are you counting the space occupied by the walls in the square footage?" asked Rex.

"Yes of course," Ralph replied. "It also includes the stairways, hallways, and basically all of the space inside of the exterior walls."

Rex smiles and says, "Nice try, Ralph! Assuming the information you gave me is correct, it'll take just a minute or two to calculate it."

How did Rex know the square footage, and what was his answer?

Check Braingle.com for the answer. ]]>

What is the probability that the coin covers the corner of four chessboard squares?

Check Braingle.com for the answer. ]]>

Check Braingle.com for the answer. ]]>

Tim reaches into Ted's bag and Tom's bag and randomly withdraws a marble from each and places them in his bag. Ted then reaches into Tim's bag and Tom's bag and randomly removes a marble from each and places them in his bag. Finally, Tom reaches into Tim's bag and Ted's bag and randomly chooses a marble from each and places them in his bag.

What is the probability that each has five different colors of marbles in their bag?

Check Braingle.com for the answer. ]]>

For example: 7 = 4 + 4 - 4/4

Now if you add the operations square root, factorial, and exponent, what is the first number counting up from zero that can't be formed? How can each number be formed?

You may use parentheses, but you may not combine fours to make 44 or 444.

(An exponent is raising a number to the power of another number such as 4^4 = 256; a factorial is the product of all the integers from 1 to the integer such as 4! = 1x2x3x4 = 24.)

Check Braingle.com for the answer. ]]>

"Honey, we're ready to eat. Can you get Hank, Ian, James and Kyle? They're in the backyard playing football. The other boys wanted to test themselves against the star quarterback," his wife called from the dining room.

The math major said, "I'll get them Dad!"

As everyone filed into the dining room, the oldest sister was rehashing the whose-school-and-major-is-better argument with her younger sister about whether Yale or Princeton was a better school and whether history or philosophy was a more useful major. The argument was practically a Christmas tradition by now.

The table was arranged with the parents at the two ends and each of the couples seated across from each other with boys seated next to girls along each side. As usual, Angelina and Danica were sitting next to their parents. Curiously, all the athletes that used a ball in their sport were sitting on the same side of the table. Christie, Electra and Edward took their seats first.

Once everyone was seated the youngest coyly observed, "I see the biologist is sitting between the two fighters but I'm sitting between the two best passers at the table."

"You'd better not make any passes yourself!" Farrah icily replied. She hadn't forgiven her sister for stealing her boyfriend when they were in high school and was not happy to see her seated next to her boyfriend now.

"Lighten up, Farrah" the biology major joked. "He wasn't even that cute."

"He was adorable!" the youngest interjected.

"Everyone's entitled to their opinion," said Brooke. "Let's eat!"

The daughter in the middle seat stood up and said, "We have an announcement to make!" After a dramatic pause she screamed "we're getting married!" and flashed the new diamond ring on her finger. The youngest sister squealed with delight at the news. Her fiance joked to his future mother-in-law, "I think she said yes just so she can wear the monogrammed sweater you gave me for Christmas." The baseball player next to her asked her fiance, "Wow, what'd that rock set you back?"

"This calls for a toast!" roared Dad.

"Oh Honey, that's wonderful news!" Mom gushed. "I just happen to have some champagne right here. Lars, I know you don't drink alcohol, but would you mind pouring some champagne for Gabrielle next to you?" the mother asked, handing the bottle to Lars on her left. "Gabrielle, please pass the bottle around," she asked and then quickly added, "But no alcohol for my three babies, or anyone under 21 for that matter. Honey, there's a store downtown that's having a sale on wedding dresses. Will you have time to go look at some wedding dresses before you leave?"

"Sure Mom," her daughter answered. "We have a late flight out, so I can do that on the day we leave."

"Michael and I are celebrating New Years Eve at the Sheraton, Waikiki," one of the girls announced.

"What a coincidence," said the boy sitting next to her. "We're celebrating New Years at the Sheraton, Los Angeles. It's within walking distance of our apartment so we won't have to worry if we drink too much."

"That sounds like a better plan than we have. Somehow, just because my car holds a lot of people, I got roped into being the designated driver for the team" Danica said, looking pointedly at her boyfriend, who gestured to the boy from Princeton saying, "he gave me the idea!"

"Girls, your grandmother will be here on Sunday," the father announced. "She'd really like to see you all."

"Sorry Dad," the business major replied, "we have to leave tomorrow. There's a huge storm predicted to hit the Eastern United States this weekend and we need to get home before they close the airports. I noticed that each couple is leaving on a different day for six days after we leave."

"Sir, we're leaving before Sunday also, so we won't be able to make it either. I'm just glad we don't have to deal with that storm" said the wrestler.

The swimmer and water polo player announced their travel plans. One of them remarked that even though his girlfriend and he were departing for Oxford University two days earlier, both couples would get home on the same day.

The physics major said "I'll be here to see grandma, but unfortunately we're heading back to California before you go look at the wedding gowns."

"Well I'm glad you'll at least be here to see your grandma, but I wish you could stay longer" the dad said. "You know you're my favorite since you were my first to major in a physical science like me," he joked. "I have a tee time at the club on Monday, it's too bad you won't be here," the father remarked to the golfer. "Kyle's got a game next week but you don't," he said to the history major's boyfriend. "How about you join me on the links?"

"Sure!" the boyfriend replied enthusiastically.

"Since we're leaving the day after him, if you've got room for two more Dad, we just happened to bring our clubs" the second oldest said, winking at her boyfriend.

"It's a foursome then!" her dad said happily.

Ian grumbled, "Hank you lucky dog, I've wanted to play that course for years!"

The boyfriend of the political science major laughed, "I'd like to play there also, but Ian, at least I won't have to travel as far as you to get another opportunity."

---------

Identify the boyfriend and his sport, the school, and major for each daughter. Name the order that the daughters were born in and the day of the week that they leave to go home. What is the seating arrangement at the dinner table?

Bonus question: what year is it?

Check Braingle.com for the answer. ]]>

"The numbers one less and one more than the number are both the product of five prime numbers. The three numbers together have thirteen prime factors, all different. The sum of the prime factors of the number is 1400."

"OK," says Ralph after a moment. "That's probably enough information to find the number with a brute-force search, is that what you expect me to do?"

"No, no, no," replies Rex. "I don't want you to do anything as inelegant as that. Here's some more information."

"The digital sum of each of the number's prime factors is prime, as is digital sum of the product of these sums. In fact, if you the reverse the digits in the product's digital sum you get a different prime number that is the digital sum of the number I'm thinking of."

Ralph takes out a pad of paper and starts jotting down some notes.

"The middle two digits in the number are its only prime digits and the number formed by the middle two digits is also prime. The number formed by the first three digits in the number is prime and its digital sum is also prime. In fact, the digital sum of the digital sum, and the digital sum of the digital sum of the digital sum of the first three numbers are also both prime."

"What number am I thinking of?" asks Rex.

Ralph jots down a few more notes and then does a couple of calculations on his calculator. He says, "OK, I know it's one of two numbers, but I don't want to factor these to figure out which one."

Rex frowns and says, "One of those numbers is divisible by 13."

Ralph smiles and tells Rex the number.

What were the two numbers and which one was the one Rex was thinking of?

Note: The "digital sum" is the sum of the digits in a number. For example, the digital sum of 247 = 2 + 4 + 7 = 13.

Check Braingle.com for the answer. ]]>

Can you tell who is the truth teller, the liar and the unreliable man by asking just three questions? Each question is directed to a single person.

Check Braingle.com for the answer. ]]>

"We each get one die, the highest die wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll again. If you get a one the second time you have to keep it."

What is each person's probability of winning?

What are the probabilities of winning if you can keep rolling until you get something besides a one?

Check Braingle.com for the answer. ]]>

"There are two dice and the goal is to have the highest total of two dice. You roll first. If you don't like your roll, then you can roll both dice again. If you roll a second time, you must keep the second roll. I'll roll second. I have to keep my first roll, but if we both roll the same number, I win."

On your first roll you roll a 7. Should you roll again or keep the 7?

Bonus question: if you play the optimal strategy, what is the probability that you will win?

Check Braingle.com for the answer. ]]>

When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.

What is the probability that the 10 friends holding hands form a single continuous circle?

Check Braingle.com for the answer. ]]>

100307124369

111824028801

433800063225

Check Braingle.com for the answer. ]]>

What is the probability that at least one person draws their own name?

Check Braingle.com for the answer. ]]>

0-1-3-2-6-7-5-4-12-_-_-_

Check Braingle.com for the answer. ]]>

"Multiply each of my daughter's age by each of her three sisters' ages. For each daughter, take the product of the three resulting numbers. Then take the product of these four results. Divide this total by the product of the four daughter's ages and discard the fractional portion. Next subtract the product of the four daughter's ages. Now divide this value by 10."

"What is the remainder?" Rex asks.

Ralph thinks about this for about a minute before answering.

Rex is disappointed that he has once again failed to stump Ralph.

What was Ralph's answer?

Check Braingle.com for the answer. ]]>

0-1-1-2-10-_____-100903245677250689568

Check Braingle.com for the answer. ]]>