Leaderboard

...inside a cube the largest square that can fit in is not coplanar with the largest circle that can fit in.

The findings of the Huygens probe indicate that Titan (Saturn's largest moon) has a nitrogenous atmosphere that periodically produces rain onto that moon's surface. Titan and Earth are the only known heavenly bodies with liquid rain. But given its hostile temperature of -180oC Titan's rain is not water, it's liquid methane. But enough of the cold facts. The exciting part of this puzzle is that in 2004 you were given a large supply of beef jerky, a warm parka, and the job of being Titan's chief in-person, feet on the ground, up close and personal, weather observer. Upon your recent return, you reported your findings on Titan's rain activity. Let's call the days on Titan that it did not rain "sunny" days, even with the constant nitrogenous smog. (You grew up in Los Angeles.) You found that sunny days on Titan were followed by another sunny Titan day 29 days out of 30, (pss = 29/30), while rainy days were followed by another rainy day with probability prr = 0.7. Like many heavenly satellites, Titan's rotation is tidally locked to its orbital period (16 Earth days.) If you were on Titan for say 9 Earth years, on about how many Titan days did you observe rain?

all identical except colour. 8 blue, 4 red

Let A be a list of n integers between 1 and k. Let B be a list of k integers between 1 and n. Prove that there's a non-empty subset of A and a (non-empty) subset of B having the same sum. Example: Say n=3, k=5 and A={3,4,5}, B={1,1,2,3,3}. Then we can find {1,3,3} is contained in B and {3,4} contained in A with the same sum (I know there're are simpler solutions in this example, it's just for demonstration).

Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second. In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?

2^3=3^1+5 2^5=3^3+5

complete this box, hint is "snake"

An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?

Two days ago, Suzy was 8. Next year, she'll be 11. How is this possible?

In a rectangular array of people, who will be taller: the tallest of the shortest people in each column, or the shortest of the tallest people in each row?

Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.

Inspired by the witty code of BobbyGo A random number generator generates integers in the range 1...n, where n is a parameter passed into the generator. The output from the generator is repeatedly passed back in as the input. If the initial input parameter is one googol (10100), find, to the nearest integer, the expected value of the number of iterations by which the generator first outputs the number 1. That is, what is the expected value of x, after running the following pseudo-code? n = 10100 x = 0 do while (n > 1) n = random(n) // Generates random integer in the range 1...n x = x + 1 end-do

At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many were there, and who were they?

You and your spouse invite four other couples to a party. During the course of the conversation, it is discovered that, prior to the party, each person except you was acquainted with a different number of the people present. Assuming the acquaintance relationship is symmetric (i.e., if you are acquainted with someone, that person is also acquainted with you), then how many people did your spouse know prior to the party? How many people did you know?

A boy has four red balls and eight blue balls. He arranges his twelve balls randomly, in a ring. What is the probability that no two red balls are adjacent?

Daddy came back from the market. He purchased two hammers. Dad said that the hammer was either $1.50 for one or $2.50 for two but either way the vendor was to make the same profit either way. How is this possible?

a b and c are digits not integers, good idea though. If they were integers there would still be smaller answer then what you have found here. can you find that answer too? I disagree with your first solution (well) since it is undefined, we don't know if the value is defined to mean min or max as it is undefined

The people living on Sesame Street all decide to buy new house numbers, so they line up at the store in order of their addresses: 1, 2, 3, . . . . If the store has 100 of each digit, what is the first address that won't be able to buy its house numbers?

From now on, the "+" symbol no longer means to combine the count of objects (e.g. 3 things plus 4 things make 7 total things would not be modeled as 3 + 4 = 7). Instead, the use of the + symbol is to show 5 + 3 = 7 to resolve the question of "how many spaces between objects are created when you line up five things and three things" (ex: t _ t _ t _ t _ t _ t _ t _ t ) and this is now to be considered addition If the other basic computational symbols maintained the same relationship to addition as they had before this new convention what would be the answers to the following problems? 4 - 3 = ? 3 x 3 = ? 9 / 3 = ? sqrt (36) = ?

What is the maximum number of Friday-the-13ths that there can be in a single year? What is the minimum number?

A reporter on New Year's Eve 1993 wanted to know, from Pat and Chris, how old they were, but felt (correctly, it turns out) that one would lie. So the reporter asked them both, "Write down your age now, your age at the end of next year, add these together, then multiply the result by 5," quickly followed by: "now add the last digit of the year you were born." They had no time to fake that last digit; Pat answered 281, while Chris announced 229. Who was lying, and what were their real ages at the time?

Every day, Ellie takes the commuter train and arrives at the station 8:30 AM, where she's immediately picked up by a car and driven to work. One day she takes the early train, arrives at the station at 7:00 AM, and begins to walk towards work. The car picks her up along the way and she gets to work 10 minutes earlier than usual. When did Ellie meet the car on this day?

List out the numbers from 1 to 150 in a vertical column. Left align all of the numbers to where the leading digit of the number is directly on top of the next number's leading digit (e.g. for the numbers 9, 10, and 11. 9 would be above 1 and that above 1 where zero would have nothing above it and 1 below it ex. ... 9 10 11 ... ) remove the nothing space above all the numbers to where the numbers are shifted up until they are at the top creating a list of new numbers. With this new list of numbers what is the probability of randomly selecting 322? 99? and 140?

If three circles are mutually tangent where one has a radius of 3cm, another has a radius of 4cm, and the last has a radius of 5cm. What is the area of the region bounded between the three circles?

Needn´t be so easy as you mean barcode_en.bmp

In sequencing DNA, technicians break up long molecules into smaller pieces because it is easier to sequence small segments than long ones. They must then reconstruct the target molecule by fitting the small segments together using overlaps as a guide. The small segments are sequenced beginning at either end in a random fashion. So, for example, the segment ATACAG may also be sequenced as GACATA. In this puzzle, I have chopped up many identical 50-long sequences into pieces of lengths 5, 6, 7, and 8. 30 of these pieces are: ATACAG TGACAT GTCTTA GTCGAGA AACGA CAAGG CAGTGTGA GTGGTGT CCGATGAC AGACAA TGTGA ATACAGTG CTGTG ACATA GTGTCG TACAGT GTCTTAG CATAA GGTGG GACTCCAG TGTGA CCAGTG TGTGACA GTGACATA TGTGGT ATTCTGA TGAATACA TAGCCG TGTGACCT CCTCA I have insured that these 30 pieces completely cover the 50-long sequence with which I started. Can you find that sequence?