During the night, snow began to fall at a constant rate. Sometime later, the highway crew began removing snow from the roads with their one plow. The rate of snow removal (by volume) was constant, and the plow moved two miles in the first hour and one mile in the second hour. How long had it been snowing before the crew started?

One day two mathematicians, Igor and Pavel, meet in the street.   "How are you? How are your sons?" asks Igor. "You have three sons as I remember, don't you? But I have forgotten their ages."

"Yes, I do have three sons," replies Pavel. "The product of their ages is equal to 36." Looking around and then pointing to a nearby house, Pavel says, "The sum of their ages is equal to the number of windows in that house."
Igor thinks for a minute and then responds, "Listen, Pavel, I cannot find the ages of your sons."

"Oh, I am very sorry", says Pavel; "I forgot to tell you that my oldest son has red hair."

Now Igor is able to find the ages of the brothers. What are their ages?

This b-day cake must be cut into eight equally-sized pieces. Cuts must be perfectly straight, however. Explain how to cut the cake into eight pieces with exactly 3 straight cuts.

Two climbers who specialize in climbing square-based Egyptian-style pyramids intend to compete by racing to the top of a pyramid which sits on a 250,000 sq. ft. base. One climber will take the easy route (along one of the corners) while the other plans to climb along the steepest path, directly up the middle of one of the faces. These two climbers will experience different angles of ascent. The question: What height pyramid will have the greatest difference in angles of ascent?

Two trains on parallel tracks pass in the night. One is a 715 ft. freight train and the other is a 275 ft. passenger train. Approximately an hour after they passed each other (it took 9 seconds to completely pass) the faster train stopped and then reversed direction. It overtook the slower train and passed it completely in 45 seconds. How fast were the two trains going?

Triangle Town is a city bounded by three straight borders called A, B, and C. The lengths of these three borders are integer numbers of miles (no fractions) with all three border lengths different. Curiously, all of the following computations yield results which are perfect squares: A+B+C, A+B-C, A-B+C, and -A+B+C. If Triangle Town has the smallest perimeter consistent with the above statements, what is the length of each of its borders?

In an alien world of 16-fingered people (eight on each hand), the hexadecimal number system is used exclusively. Interestingly, their coins are denominated 1, 5, 10, 25 and 50 just like ours, except that their coins' values are hexadecimal (i.e. their 10-cent coin can be exchanged for 16 of their 1-cent coins). Furthermore, they love to gamble as evidenced by their toll bridge, which instead of charging a fixed toll, flashes the toll as a random number from 1 through 100, inclusive, and hexadecimal, of course. To use the exact-change lane, how many coins of each denomination must a traveler carry in order to have the least total value of coins and still be able to exactly pay any toll?

What is the minimum number of knights that is required so that every square on a standard 8 x 8 chessboard is either occupied by a knight or else threatened by a knight?   A square is threatened if a knight can move to that square.   Recall that a knight moves two squares forward, back, right, or left, and then one square perpendicular to that direction, landing on a square opposite in color to its starting point.   The move can occur even if intervening squares are occupied.

Prof. Peek is pleased with the new extension telephone number in his office because it has four digits, the middle two of which are identical. "Like my name", he exclaims! The repeated digit is also the first digit of his secretary Miss Eagle's new four-digit number. Moreover, Peek's first digit is the same as the first digit of Dr. Sparrow's new four-digit number.

If you interchange the first and last digits of Dr. Sparrow's number, you get Miss Eagle's number. If you subtract Sparrow's number from Eagle's, you get Peek's.

So what is Prof. Peek's new extension phone number?

A Philosophy professor and his favorite student entered a railroad tunnel, looking for the meaning of life. When they were two-fifths of the way in, they heard a train coming behind them. The professor, being wiser, made a quick calculation and then decided to run back toward the entrance, just barely getting out as the train entered the tunnel. His student chose the longer way, and he escaped at the opposite end just as the train left the tunnel. Both prof and student ran at 20 km/hr. How fast was the train going?

Two men are about to play a game on a chess board using only two pieces. The first player has a queen, and the second player has a knight. Here is how the game is played ... Both players close their eyes while the first player places his queen on the board at random (all positions being equally likely)and then opens his eyes. It is now the second player's turn, and he gets two chances to capture the queen in this turn. With his eyes still closed, he places his knight on the board at random and then opens his eyes. If the initial placement of his knight did not capture the queen, he completes his turn by moving his knight (and possibly capturing the queen). What is the likelihood (expressed as a percentage) that the second player will capture his opponent's queen?

Gary and Vadim shared an apartment in a dormitory building on campus. One day, G needed a battery for his remote. And so, while Vadim was sleeping, he took the battery out of their only clock. When Vadim awoke, he quickly discovered the dastardly deed, and inserted a new battery. Not knowing the correct time, he looked out the window, estimated the position of the moon in the sky, and then set their clock to 6:31 PM-VST (Vadim Std Time). He immediately left the room and walked to visit friends. Upon arriving, he noticed that the time was exactly 6:33 PM-GMT. He stayed for exactly one hour and then walked back to his room, arriving there at 8:01 PM-VST. Vadim looked at his clock, thought about the situation for a second or two, and then correctly reset it to ___ PM-GMT.

To what time (GMT) did he reset the clock?

Claudia has 25 diamonds. Twenty four (24) are real, and one is an imitation. All of them are of equal weight except for the imitation which is slightly lighter than the real diamonds. If Claudia decides to use a balance scale to find the imitation, with luck she could find it with a single weighing (she could randomly select two stones to weigh, one of which is the imitation). Without luck, it will take her more than a single weighing. It should NEVER take her more than N weighings, however.   What is the smallest N? _____ Explain.

The number 3,435 = 3^3 + 4^4 +3^3 + 5^5 where ^ indicates exponentiation. That is, it is equal to the sum of its digits each raised to that digit's power. Find the next larger such number. [use the convention 0^0 = 0]

You are boiling a chicken in a pot, and you know that it should be boiled for 45 minutes. Unfortunately, you do not have a clock, and the boiling has just begun. How can you use two one-hour candles to measure the required cooking time? You are not allowed to use any measuring devices (no rulers, no scales, etc.) other than the candles, themselves

Ursula has 36 cloth napkins. Eleven are red, thirteen orange, five yellow, two green, and five blue. From this pile, she plans to select and tie three napkins together, end-to-end. How many essentially-different color combinations can she create without having two napkins of the same color tied next to each other?

Buses leave Boston for New York City every hour on the hour, and return from New York City to Boston every hour on the half-hour. All buses use the same highway, and the trip takes five hours each way. As you ride from Boston to NYC, how many returning buses would you pass?

Below is a quiz attributed to Albert Einstein. It is reported that he said that 98% of the people in the world cannot solve this problem. Are you among the other 2%?
Here are the facts: There are 5 houses in 5 different colors. In each house lives a person with a different nationality. These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

I just returned from shopping at the North Campus Book Store. I was going to purchase an inexpensive pen, and I found that I could pay for it using exactly four standard U.S. coins, but not fewer. ILya wanted one too, and he told me that I could purchase a pair of pens with a minimum of six coins. Max convinced me to buy one for him, too, by pointing out that I could purchase three pens with just two coins. What was the price of a pen?

Professors from PL, ME, CE, CN, and EE Departments and their wives recently sat together at a large circular table in the main UMASS-Lowell Dining Hall. The seats were so arranged that the men and women alternated and each woman was three places distant from her husband. The wife of the CE professor sat at the right of the Plastics professor. The EE professor sat two places to the left of the CE professor, and the wife of the EE professor sat two places to the right of the wife of the ME professor. If the wife of the Plastics professor looked to her left, who would she have seen sitting next to her?

Every Challenge should contain a cryptic. This one is special because it is not solvable in base-10, despite the wording. Your job is to solve it in the smallest base for which a solution exists. The usual rules of cryptics apply (e.g. None of the leading digits are zeros).