Actuarial Puzzles

  • Monthly Puzzler – May 2015

    Posted:
    Aerial Dogfight Rematch May 2015 Snoopy and the Red Baron fly past each other only inches apart, barely missing a head-on midair collision. Both are armed with laser pointers mounted on their planes that point only in the direction of motion, at zero angle of attack. Both fly at constant speeds but the Red Baron flies twice as fast as Snoopy. Read More
  • GPS in Flatland Solution – February 2015

    Posted:
    In this puzzle, Flatland has set up three fixed GPS broadcast stations (A, B and C) on the vertices of an equilateral triangle with edges of length 100 kilometers. When Richard leaves his house in Flatland to visit Roger his GPS receiver gets a time signal of exactly 7 a.m. Read More
  • Monthly Puzzler – April 2015

    Posted:
    The Shape of Melting Ice April 2015 Suppose a cube of ice completely melts in exactly one hour. Throughout the melting process, the temperature inside the entire ice cube remains uniform at just a tiny amount below the freezing point. The external environment maintains a temperature just above the freezing point. Read More
  • War of Attrition Solution – November 2014

    Posted:
    In this puzzle, the Blue Army and the Red Army fight until one side is completely annihilated. At each instant, the rate of casualties experienced by each army is equal to the surviving size of the other army times the other army’s firepower constant. The Blue Army wins with 85% of its initial force surviving. Read More
  • Monthly Puzzler – February 2015

    Posted:
    GPS in Flatland February 2015 Flatland, a two-dimensional Euclidean world, has set up three fixed GPS broadcast stations. The stations, A, B and C, are located on the vertices of an equilateral triangle with edges of length 100 kilometers. When Richard leaves his house in Flatland to visit Roger, his GPS receiver gets a time signal of exactly 7 a. Read More
  • Soccer Tournament Scheduling Solution – January 2015

    Posted:
    Last month, we posted a problem which asked for a schedule in the minimal number of weeks for a soccer tournament where each of 10 teams plays each other team exactly once, no team plays more than once each week, and there are no more than four games a week. One actuary observes that there are 10×9/2, or 45, games, so with at most four games a week, it will take at least 12 weeks for the tournament. He gives one such schedule below. Read More
  • Betting on Squares and Cubes Solution – September 2014

    Posted:
    In this puzzle, 10,000 integers were selected randomly from the set 1 to 10^(10^(10^(10^(10^10)))). For each integer that was divisible by a square (>1) but not by a cube (>1), Bernhard would pay 3.9 thaler, and receive 1 thaler for every other integer. Read More
  • Monthly Puzzler – January 2015

    Posted:
    Soccer Tournament Scheduling January 2015 There are 10 teams. Because of limited field space, only eight teams can play each week (four games maximum in any week). No team can play more than once a week. Read More
  • Monthly Puzzler – December 2014

    Posted:
    Lost at Sea December 2014 Captain Ron is stranded alone in a small motorized inflatable boat in the middle of the Pacific Ocean near the Equator. He is out of food and water. All he has is a compass, enough fuel to last about 75 minutes, and, of course, a bottle of rum which is nearly empty. Read More
  • Monthly Puzzler – November 2014

    Posted:
    The Blue Army and the Red Army commence fighting and continue, without reinforcements or replacements, until one side is completely annihilated. At any given instant after fighting begins the deterministic and continuous rate at which members of one army are “eliminated” is equal to the other army’s “firepower constant,” a positive number, times the surviving size of the other army at that time. Read More
  • The Spill Free Mug Solution – October 2014

    Posted:
    Last month, we posed a problem about a restaurant selling 20 ounce drinks—carousing customers were spilling a lot of the drink. In the course of clinking mugs and raising toasts, the mugs are often tilted at up to 45 degrees from vertical. Read More
  • Paranormal Logic Solution – July 2014

    Posted:
    This puzzle, which appeared in the July/August issue, listed six logical constraints on the existence of people who might have been abducted by a UFO, seen Bigfoot, seen Elvis last year, and might be able to levitate, produce cold fusion, and/or have ESP. Read More
  • Monthly Puzzler - October 2014

    Posted:
    Monthly Puzzler – October 2014 The Spill Free Mug Here’s a problem a local bar had recently when selling 20-ounce soda mugs: carousing customers were spilling a lot of the drinks. In the course of clinking mugs and raising toasts, the mugs are often tilted at up to 45 degrees from vertical. The establishment redesigned the mug, making the inside a cylinder, open at the top. Read More
  • Monthly Puzzler – September 2014

    Posted:
    Augustus proposes a hypothetical betting game to be played between Bernhard and Carl. Augustus will randomly pick 10,000 integers from the set from 1 to N where N =10^(10^(10^(10^(10^10)))). For each of the numbers selected that is either divisible by the cube of an integer greater than 1 or not divisible by the square of an integer greater than 1, Carl will pay Bernhard 1 thaler. Read More
  • The Logic of Counting Liars Solution – August 2014

    Posted:
    This puzzlement, from Jon Evans, was four variants on the standard truth-teller versus liar puzzles. There are n > 1 attendees, numbered 1 through n, at a CAS ethics seminar. Each attendee is either a liar, who only makes false statements, or a truth-teller, who only makes true statements. Read More
  • It Only Takes a Googolplex to Run Solution – June 2014

    Posted:
    In this puzzle, a simulation that started on Thursday finished after a few weeks on a Tuesday. A more general version of the simulation will take a googolplex, or 10^(10^100), times as many days to finish. The question is: If the new simulation begins on that Tuesday, on what day of the week will it finish? Read More
  • Monthly Puzzler – August 2014

    Posted:
    You are in a country where there are only truth-tellers, who always tell the truth, and liars, who always lie. You cannot tell them apart. You’re on your way back the village and come to a fork in the road. One way leads to the village and the other to certain death, or something dire in any event. There’s no sign, and you don’t know which way leads to the village. There’s a native standing there. Read More
  • Monthly Puzzler – July 2014

    Posted:
    Paranormal Logic July 2014 Dr. Pons Vallee Martin, of The Institute for the New Age Enlightened Reform of the Scientific Method, has come to the following conclusions: a) Everyone who saw Elvis last year has seen Bigfoot. b) If someone cannot levitate, that person cannot produce cold fusion. Read More
  • Don’t Run Over the Bicycle Solution – May 2014

    Posted:
    The puzzle was as follows:  On a clear dark night, you are driving your car with your headlights on along a narrow but straight country road.  A stopped bicycle 30 meters away, with no lights of its own, no reflectors, and a rather dull paint job, would be visible with 10 times the minimum brightness for you to notice an object.  Suppose you are driving 30 meters per second and need to notice any such stopped bicycle at least two seconds in advance to safely avoid a tragic collision. Read More
  • Monthly Puzzler – June 2014

    Posted:
    A computer science student runs a simulation that starts on a Thursday and finishes a few weeks later on a Tuesday. The student then starts a more general simulation that same Tuesday. Read More
  • Monthly Puzzler - May 2014

    Posted:
    Don’t Run Over the Bicycle On a clear dark night you are driving your car with your headlights on along a narrow but straight country road. A stopped bicycle 30 meters away, with no lights of its own, no reflectors, and a rather dull paint job, would be visible with 10 times the minimum brightness for you to notice an object. Read More
  • Public Health and Urban Planning Solution – April 2014

    Posted:
    This puzzle involved nurses making public health visits in a city. Nurses visit one resident at a time, leaving from one of 100 clinics (the one closest to the resident) and returning to the same clinic before visiting the next resident. Total travel distance for the nurses to visit each resident is 1 million miles. Increasing the number of clinics to 150 reduced the average round trip travel by two-tenths of a mile. What is the population of the city and what is the area of the city? Read More
  • Hot and Cold Solution – March 2014

    Posted:
    The uniform temperature change implies the following:
      Winter average temperature = coldest + (hottest - coldest)/8
      Summer average temperature = hottest - (hottest - coldest)/8
    Read More
  • Monthly Puzzler - April 2014

    Posted:
    The roads in a large city all run either north-south or east-west in a dense grid. There are 100 public health clinics spread across the city in a pattern designed to minimize the average distance to the nearest clinic. Read More
  • Monthly Puzzler - March 2014

    Posted:
    Astronomers have been discovering extrasolar planets at a fantastic rate. He says one is a planet with the catchy name PV/Nk, which has exactly four equally long seasons: winter, spring, summer, and fall. From the Coldest Day which is in the middle of winter, to the Hottest Day which is in the middle of summer, the temperature increases at a uniform rate. Read More
  • Aerial Dogfight Solution – February 2014

    Posted:
    In this puzzle, Snoopy and the Red Baron fly past each other in opposite directions, turning hard left and hard right, respectively. The first one to shine his laser pointer, fixed on a forward pointing mount, on the other wins. David Uhland observes that the key to this puzzle is that the pilot with the smaller turning radius always wins. Read More
  • Monthly Puzzler- February 2014

    Posted:
    Aerial Dogfight February 2014 Snoopy and the Red Baron fly past each other only inches apart, barely missing a head-on midair collision. Both are armed with laser pointers mounted on their planes that point only in the direction of motion, at zero angle of attack. Both fly at constant speeds but the Red Baron flies twice as fast as Snoopy. Read More
  • Monthly Puzzler - January 2014

    Posted:
    Puzzler: Flying Saucers Encircle the Earth January 2014 Aliens deploy flying saucers around the Earth. The aliens believe the Earth is a perfect sphere with radius 6,400 kilometers. They design the formation so that at any time at least one of the saucers can shine a laser (hopefully just a friendly low-power scanning laser! Read More