Puzzles

• Apple Tree Line Puzzle [McCoy, 11/07/1997]
  Plant 13 apple trees in nine rows with four apple trees in each row.

• Arrange 7 Points in a Plane... [Lesko, 10/05/1998]
  Arrange 7 points in a plane so that if any three are chosen, at least 2 of them will be a unit distance apart.

• Calendar Trick [Simms, 12/04/1996]
  Given a day, month, and year, is there a formula you can use to find the day of the week?

• Diagonals and Tiles [Kamie, 11/17/2001]
  Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through?

• Dimensional Analysis [Katie, 10/06/2001]
  Mr. R wants to give all of his chemistry students enough chocolate to make them goofy for the rest of the day. It's a known fact that it takes 47 chocolate chips to make a student goofy...

• Finding One Coin of 12 in 3 Steps [Schwartz, 8/6/1996]
  Given a pile of twelve coins of equal size with one of a different weight, in three weighings find the unequal coin...

• Formula for Nim [Kentaro, 02/22/2002]
  Is there a formula for the game of Nim?

• The Four Fours - an Ancient Problem [Tibbitts, 10/02/1997]
  The problem allows you to use only four fours and as many operands as you like in order to create mathematical sums that equal the numbers from 1 to as high as you can go.

• Grid with 14 Dots [Schuldenfrei, 11/10/1997]
  Put dots in 14 squares in a 6 by 6 grid. There must be an even number of dots in every row and column (zero is even). Is there a rule for building solutions to this problem?

• Hands of a Clock [Porter, 10/10/1997]
  How many times do the hour and minute hands cross in a 12-hour period of time?

• Look-and-Say Sequence [Vanessa, 02/14/2002]
  I can't find the next six numbers: 1, 11, 21, 1211, 111221, ...

• Lucky Seven Fractions Puzzle [Victor, 12/22/2001]
  Put numbers 1-9 in order to make the equation correct: XX/XXX+XX/XX=7.

• Magic Pentagon [Ramona, 12/02/2001]
  Using the numbers 1-10 once each, make the sums of the three circles equal.

• Mensa: Numbering for an Alternate World [Wernke, 5/25/1995]
  In a parallel universe, the numbering system in use is based on the 26-character Roman alphabet. In this universe you are driving from New York to San Francisco. A road sign indicates you are BBQ miles from San Francisco. Are you closer to...

• Number of Squares in an NxN Square [Fengh, 7/29/1996]
  How many squares are there in an 8 x 8 square? How many rectangles are there?

• Proving that 1 + 1 = 3 [Axel, 11/18/1995]
  How can I show that 1 + 1 = 3 ?

• Remainders of 1, 2, 3, 4 [Laura, 10/09/2001]
  Find the smallest whole number that when divided by 5, 7, 9, and 11 gives remainders of 1, 2, 3, and 4 respectively.

• Remainder Problem [Virginia, 10/27/2001]
  What number less than 500 produces remainder 4 when divided by 5, remainder 7 when divided by 9, and remainder 9 when divided by 11?

• The Traveling Bee [Emerling, 09/18/1998]
  If a bee travels between two trains that are moving at 30 and 20 mi/hr respectively, starting from 50 mi apart, how far does the bee travel?

• Weird Fraction Behavior? [Neill, 11/4/1994]
  If you look at the fractions (16/64) and (19/95), you may notice that if you cancel out the second number in the numerator with the first number in the denominator the fraction remaining is equivalent to that of the original equation. Ex. in the fraction (16/64) if you cancel out the second number in the numerator (6) with the first number in the denominator (6), you end up with (1/4), which is equal to (16/64). The only restrictions are that the numbers canceling must be the same number, as in the above example (a 6 for a 6). Also the numbers for the original fraction are restricted to two digits (10-99). How many more of these numbers can you find?

• Stack of Oranges [Zaker, 1/9/1995]
  A stack of oranges is compactly arranged so the bottom layer consists of oranes in an equilateral triangle with n oranges on a side. The layer next to the bottom consists of n-1 oranges on a side. This pattern continues upward with one orange on the top. How many oranges are there?

• Bananas by Camelback [Tseng, 2/12/1995]
  There is a camel that needs to travel 1000 miles to the nearest city. The camel has 3000 bananas but can only carry 1000 at a time...

• When will Ramadan fall across 3 months? [Szilak, 3/5/1995]
  This year the Muslim holy month of Ramadan fell across 3 months of the western calendar. It began 31 Jan & ended 1 Mar....

• A Geometry and a Logic Problem [Marsville, 3/11/1995]
  Problem 1: A cylindrical hole six inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? Problem 2: The classical stay-switch problem.

• Logic - Liars & Truthtellers (What Question Does She Ask?) [Marsville, 3/12/1995]
  A logician vacationing in the South Seas finds herself on an island inhabited by the two proverbial tribes of liars and truth-tellers.

• Zeno's Paradox [Gut, 10/19/1995]
  At eleven o'clock I put ten balls numbered 1,2, ...10 in a box and immediately take out the ball numbered 1. At eleven thirty I put balls numbered 11 through 20 into the box and take out the ball numbered 2. At eleven forty-five I put balls numbered 21 through 30 into the box and take out the ball numbered 3. This continues at time intervals that are half of the preceding one. How many balls are in the box at twelve o'clock?

• Disproving that One is Equal to Two [Chamberlain, 11/13/1995]
  I'm trying to disprove a proof that says 1 is equal to two. I've been struggling with finding the error in my logic for quite some time now, but can't seem to quite get where I messed up.

• Traveling Salesman Problem [Fws, 12/3/1995]
  Find a procedure that describes how to find the minimum distance between any 15 randomly placed dots.

• The Prisoners' Dilemma [Tim, 12/8/1995]
  I'm looking for a paper - or some material - about "the prisoners' problem."

• Geometry Puzzles [Creswell, 12/18/1995]
  A student asks Dr. Math for help in finding the correct combinations of numbers to solve two puzzles.

• Divisibility Word Problem [Soebadi, 1/27/1996]
  Arrange the digits 0 to 9 such that the number formed by the first digit is divisible by 1, the number formed by the first two digits is divisible by 2, that formed by the first three digits divisible by 3, and so forth; thus the number formed by the first 9 digits will be divisible by 9 and that formed by all 10 digits divisible by 10.

• Primes and Number Riddles [DRLFamily, 4/15/1996]
  A prime number riddle.

• Magic Square [Steve, 5/16/1996]
  How can I make a magic square?

• Feeding Oxen [Ocastill, 6/26/1996]
  We have 3 pastures with grass of identical height, density and growth rate... How many oxen can be fed for 18 weeks?

• Magic Square [Kcl, 7/4/1996]
  How do you make a magic square?

• Squares of Positive Integers [Davsmy, 8/13/1996]
  The positive integers a and b: the numbers 15a+16b and 16a-15b are both squares of positive integers...

• 100 Lockers, 100 Students [5591121, 8/16/1996]
  There are 100 closed lockers in a hallway, and 100 students. Student 1 walks down the hall, opening every locker...

• Shuffling Cards [Grende, 8/26/1996]
  How many 'perfect shuffles' does it take to get the cards back in the order you started?

• Magic Star Puzzle [McGillivray, 9/2/1996]
  I have a star puzzle shaped like 2 triangles with 4 circles in each row. We have to use the integers 1 to 12 and the sum of each row must be the same...

• How Many Friday the 13ths [Smith, 9/12/1996]
  Is there a way to figure how many Friday the 13ths can occur in a given year?

• Bouncing Cue Ball [Nichole, 10/29/1996]
  A cue ball is launched at an angle of 45 degrees from the lower left corner of a pool table and ends up in the lower right corner. What rule will predict which corner the ball will hit? What patterns are involved?

• Maximizing Output of a Restricted Function [Lovelace, 11/1/1996]
  Create a function whose domain is restricted to complex numbers but whose range is real, that is, non-constant, has no constant term, and contains no number greater than 3.

• Formula for Factors of a Number [Daniel, 11/3/1996]
  How many triangles can you draw on a square grid of dots of size x*x?

• Triangles within a Triangle [Jensen, 11/10/1996]
  If multiple small equilateral triangles are drawn within a larger one, what is the relation between the number of small triangles lying on the base of the big triangle and the total number contained within the big triangle?

• 33 Pearls Problem [Fletcher, 11/14/1996]
  On a string of 33 pearls, the middle pearl is the most expensive one - find its value.

• Monkeys in the Jungle [Berkman, 11/18/1996]
  How can a group of hungry monkeys carry the bananas to their friends across the jungle? They want to arrive with the maximum number uneaten.

• Simultaneous Equations with Integral Solutions [Klasic, 11/29/1996]
  What kind of a math project could I do with magic squares?

• Hole in a Sphere [Klein, 12/30/1996]
  When you bore a 6 inch cylindrical hole through the center of a sphere, what is the volume of the remaining solid?

• Crypto-Number Puzzle [Ivan, 01/21/1997]
  A Pascal program to find numerical values for the letters in: ONE + TWO + TWO + THREE + THREE = ELEVEN.

• Number Puzzle [Kuo, 02/12/1997]
  Find a 9-digit number in which the 1st digit is the number of 0's, the 2nd digit is the number of 1's..., and the 9th digit is the number of 8's.

• Opening and Closing 1000 Lockers [Atsang, 03/16/1997]
  There are 1000 closed lockers and 1000 students. The first student opens every locker; the second student reverses every other locker...

• Averaging 30 Miles Per Hour [Wissel, 03/17/1997]
  If for half the distance of a trip you travel at 15 mph, what will your speed have to be for the rest of the trip for you to average 30 mph?

• Last Digit of a Number [Raff, 04/14/1997]
  What is the last digit in (1996^1997)-(1997^1996)?

• Crossing the Bridge [Comfort, 05/12/1997]
  Four men want to cross a bridge but only two may cross at a time...

• Formula for the Day of the Week [Durling, 05/21/1997]
  Please tell us what day of the week the Declaration of Independence was signed on, and the formula to determine it.

• Powers of Two [Cofre, 05/29/1997]
  Prove that every power of two has a multiple whose decimal expansion has only digits 1 and 2.

• Winning at NIM [Wilson, 06/09/1997]
  How do you ensure that you win the game of NIM?

• Letter Puzzle [Ziva, 06/15/1997]
  Find a four digit number such that 4(ABCD) = DCBA.

• Squares, Rectangles on a Chessboard [Taur, 08/14/1997]
  How many squares are there on a chessboard? How many rectangles?

• How Old is Korinth? [Phillips, 09/09/1997]
  Korinth is twice as old as Marin was when Korinth was as old as Marin is now. Marin is 18.

• Weight of Each Bale of Hay [Getman, 09/26/1997]
  Five bales of hay are weighed in all possible combinations of two...

• Linear Equations and Functions [Hartman, 10/11/1997]
  The digits of a positive 2-digit integer N are interchanged to form an integer K. Find all possibilities for N... the average of N, K, and 35 is 30.

• Tower of Hanoi [Bankston, 10/16/1997]
  I'm looking for a mathematical solution, not a trial-and-error one.

• 1000 Lockers [Thorsheim, 11/06/1997]
  The 1st student opens all 1000 lockers, the 2nd student closes lockers 2,4,6,8,10, etc., the 3rd student opens lockers closed and closes lockers open on lockers 3,6,9,12,15...

• Perilous Ping-Pong [Stone, 11/14/1997]
  Weigh the balls to find the one that's different...

• Towers of Hanoi Puzzle: 3 Pegs, n Discs... [Lauren, 11/15/1997]
  We are told to find out the least number of moves it takes to get three discs in size order onto the third peg from the first.

• Locker Problem [Boyer, 11/21/1997]
  There are 1,000 lockers numbered from 1 through 1,000. The first student opens all the doors; the second student closes all the doors with even numbers...

• Three Weights [MacDougall, 12/07/1997]
  A boy selling fruits has only three weights, but with them he can weigh any whole number of pounds from 1 pound to 13 pounds inclusive. What three weights does he have?

• 3 Weighings Problem [Midkiff, 12/09/1997]
  You have a balance scale and 12 balls that all look and weigh the same except one...

• Birthday Probabilities [Fred, 12/09/1997]
  What's the minimum number of people you need in order for the probability that two of them were born on the same day of the week to be 50 percent?

• Weighing Bales of Hay [Mays, 12/10/1997]
  Five bales of hay are weighed in all possible combinations of two...

• Rameses' Pyramid [Mckeill, 12/10/1997]
  A pyramid-building puzzle.

• Coconut and Monkey Puzzle [Koestler, 12/18/1997]
  How many coconuts were in the original pile?

• Ben and Bill [Shamala, 12/21/1997]
  Bill + Ben's age = 91. Bill is twice as old as Ben was when Bill was as old as Ben is now.

• Indefinite Series, Perfect Squares [Connie, 01/01/1998]
  Across the first row of an 11-column table are the numbers 1991, 1992, 1993, .... 2000, 2001.

• Money Puzzle [Vedachal, 01/05/1998]
  A man goes to the bank and asks for x dollars and y cents.

• Math Puzzle: Day of the Week [Griffin, 02/04/1998]
  Why does the following math problem work, irrespective of the number you use 0-7 for the day of the week?

• The Four Doors of Xanth [Goodwin, 02/11/1998]
  Each door conceals one item: a treasure, a rope, a key, and a lantern. You must find all four items in a particular order to keep the treasure.

• Algorithms for the Knapsack Problem [Okoh, 04/08/1998]
  I need to find an algorithm to solve the Knapsack Problem, where a person needs to fit as many toys in his knapsack as possible.

• Constructing a Conditional Table [Brown, 04/14/1998]
  I have a table that is 5 columns wide and 7 rows high and contains either a 0 or a 1 in each cell...

• Squares on a Checkerboard [Moore, 04/26/1998]
  How many squares are there on a checkerboard?

• Cockroach Traveling Along an Elastic Tightrope [Fields, 05/15/1998]
  Finding the harmonic series in a problem of related rates.

• Two Mathematicians Problem [Tuncel, 05/18/1998]
  One mathematician is give the sum of integers X and Y, and another is given their product... what are the numbers?

• Digital Clock Lights [Rasheed, 06/29/1998]
  If the only light source in a room is a digital alarm clock (red LEDs), at what time is the room the darkest? Lightest?

• Knights of the Round Table [Lou, 07/01/1998]
  If x knights are sitting at a round table, and every other one is removed, who is the last one left sitting at the table?

• Crossing a Desert with 45 Watermelons [Williams, 07/08/1998]
  A boy carries 45 watermelons across a 15 mile desert, 15 at a time, eating 1 per mile. What is the most he can carry to the other side?

• Winning at NIM [Tyrrell, 07/25/1998]
  In a game of NIM, there are three rows of 5, 4, and 3 sticks respectively. Picking up as many as you want in a row, how do you win?

• The Value of a Word [Gordon, 08/25/1998]
  Think of a word that equals one dollar. The key is: a=.01, b=.02, c=.03, ....

• Employee Scheduling [Lindsay, 09/22/1998]
  Can you help me make a schedule to staff an ice cream parlor?

• A Circular Massacre [Kurczak, 09/25/1998]
  Ten thousand sailors are arranged in a circle; starting with the first one, every other sailor is pushed overboard ....

• Bachet's Theorem [Deamer, 10/08/1998]
  My maths teacher said that a mathematician discovered that you can make any number by adding together a combination of no more than 4 square numbers.

• Coconut Piles [Stillman, 10/12/1998]
  What is the least number of coconuts they could have started with?

• The Truel [Sabina, 10/13/1998]
  A truel is a duel with three participants, rather than two. Whom should Mr. Black shoot first to survive?

• Pool Table Algebra [Roland, 10/21/1998]
  The y-axis, x-axis, x = 6, and y = 12 determine the sides of a pool table. Follow the path of a ball starting at the point (3,8).

• Abstract Algebra and Puzzles [Clarke, 10/31/1998]
  Do you have any ideas for projects that involve abstract algebra?

• Rubik's Cube [Smith, 12/03/1998]
  Can you explain some of the math behind the Rubik's Cube?

• Who Made Which Toys? [Katie, 12/21/1998]
  A math logic problem, from a rhyme describing Santa's toymakers.

• Connecting the Boxes [Mainprize, 12/28/1998]
  I have an arrangement of boxes and am trying to draw one continuous line connecting them all. Can this be done?

• Adding and Multiplying to Get 7.11 [Sam, 01/13/1999]
  What four monetary values, when added or multiplied, equal $7.11? (Find A, B, C, D, such that A+B+C+D = A*B*C*D = 7.11.)

• Moving Knights on a Chessboard [Gibson, 01/27/1999]
  Given 4 knights at the 4 corners of a 3-by-3 chessboard, can the knights exchange places if they can move only in the following way?

• Russian Nim [Kevin, 02/15/1999]
  Strategies for winning at Russian Nim (the "20" game).

• A Special Ten-digit Number [Donna, 02/17/1999]
  Create a ten-digit number that meets some special conditions...

• Rubik's Cube [Connie, 02/18/1999]
  Sequences of turns for solving Rubik's cube.

• Cutting a Cylinder out of a Sphere [Minesh, 02/25/1999]
  What is the remaining volume after a cylinder of length 6" has been cut through the centre of a sphere?

• Dartboard Scoring [Meaghan, 03/01/1999]
  Find the highest score you cannot get with the center worth 9 points and the outer ring worth 4.

• Hands on a Clock [Logan, 04/05/1999]
  At what time (if any) do the three hands of a clock trisect its face?

• Alphametric Problem [Gracefield, 04/06/1999]
  How do you solve a four-part alphametric where each letter represents a different digit?

• A Fibonacci Jigsaw Puzzle [Laik, 04/29/1999]
  Why is the area of our rectangle, formed from a square, 65 when the square's area was 64?

• Arithmetic Code [John , 05/09/1999]
  Break the code, given that each of the following is true in ordinary base ten arithmetic...

• Counting Triangles [Michael, 05/27/1999]
  In a large triangle with 36 small ones inside, how many triangles are there in all?

• Let's Make a Deal Probability [McGinn, 06/01/1999]
  In "Let's Make a Deal," does Monty's showing you a door, or his knowing which door the prize is behind, affect the probability?

• More Monkeys and Nuts [Holt, 06/07/1999]
  How can I solve this variation on the monkeys and the nuts puzzle?

• Formula for Easter [John, 06/12/1999]
  Is there a formula for finding the month and the day on which Easter falls in a given year?

• Counting Rectangles Cut By a Diagonal [Ben, 06/15/1999]
  How can we find an equation for the number of unit squares that are cut by a line going from corner to corner on a rectangle?

• Prices in Store 88 [Fu, 07/05/1999]
  In Store 88 they sell exactly ten items, some items with the same price as others, but the only the digit on the price tags of each item is 8...

• Handshake Problem Variant [Bixler, 07/08/1999]
  Five couples go to a party and start shaking hands. One of the men shouts, "Stop! How many hands did you shake?" Every person gives a different answer...

• Grains of Wheat [Khalafalla, 07/14/1999]
  The person who invented the game of chess was said to have been offered any payment he wanted... How much wheat did he receive?

• Find the 3-Digit Values A, B and C [Goorman, 08/08/1999]
  How can I determine the 3-digit integers a, b, and c when the ratio a:b:c is 1:3:5 and the digits of a, b, and c are 1,2,3,...,9, each appearing exactly once?

• Wile E. Coyote Lands in the River [Saddie, 08/20/1999]
  Wile E. Coyote is standing on a springboard atop a high cliff. Road- runner drops a boulder on the other end of the springboard, sending Wile up at an initial velocity of 4 m/s. At what time will he land in the river, 120 m below the top cliff?

• Change for a Dollar [Sarah, 11/05/1999]
  When changing a dollar bill, you can give 1 coin (1 silver dollar), 2 coins (2 half-dollars), 3 coins (2 quarters and 1 half-dollar), and so on. What is the least positive number of coins that is impossible to give as change for a dollar bill?

• Closest Palindromic Dates [Hessam, 02/07/2000]
  Using the abbrevation date.month.year, what are the two palindromic dates closest together in the 1900s?

• The Pharaoh's Will [Balalis, 05/16/2000]
  As he lay dying, the Pharaoh proclaimed: "I bequeath 1/3 of my estate to my oldest child; 1/4 of my estate to the next oldest child; and to each succeeding child, except the youngest, the next unit fraction of my estate; and to the youngest the remainder."

• Left-Sided Rhombuses in a Larger Rhombus [Wright, 05/22/2000]
  How many left-sided, right-sided, and vertical rhombuses can be found in a larger NxN rhombus?

• Dividing the Prize Money [Sawbridge, 05/24/2000]
  Mrs. Shoe gave her prize winnings to her children in order... and all the prize money was divided equally amongst her children. How many children were there?

• Solving a Math Poem [Amber, 05/24/2000]
  Take five times which plus half of what, and make the square of what you've got...

• 9 x HATBOX = 4 x BOXHAT [Stribling, 05/30/2000]
  What is the solution to the cryptogram: 9 x HATBOX = 4 x BOXHAT?

• Nim [Winarto, 09/26/2000]
  What is the principle of Nim and what is its application?

• Hidden Faces in a Set of Cubes [Roden, 10/04/2000]
  Can you give us a hint for a formula that will tell you the number of hidden faces in an arrangement of a cubes if you know the number of visible faces?

• Towers of Hanoi [Rakesh, 10/08/2000]
  Can you prove the formula 2^n - 1 for the least number of moves it takes to move all n discs to another peg in Towers of Hanoi?

• Six-Card Trick [Marsh, 10/25/2000]
  A Volunteer writes different numbers from 1 to 125 on six cards, and keeps one. The Host arranges the others in some order and gives them to the Partner, who then says the number on the missing card. How?

• Multiplication Using +, -, and 1/x [Silverman, 10/25/2000]
  Suppose you had a calculator with only the +, -, and 1/x operator buttons. Could you do multiplication with it?

• Quickly Finding the Day of the Week [Anand, 11/14/2000]
  Today is November 14, 2000, a Tuesday. What day of the week was November 14, 1901?

• Box A or Box B? [Joe, 11/21/2000]
  A professor shows you two boxes. Box A has $10K; Box B has $1M or $0. You can take Box B only or both boxes... Which do you choose?

• EVE/DID = .TALKTALKTALK... [Stuart, 11/21/2000]
  In the equation EVE/DID = .TALKTALKTALK... each letter corresponds to a different number, and EVE/DID is in lowest terms. What does each letter stand for?

• Unit Fractions and the Greedy Algorithm [Foon, 12/27/2000]
  How can I represent 2000/2001 as the sum of unit fractions?

• Divisibility Puzzle [Li, 01/22/2001]
  The leftmost digit of an integer of length digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either a or b. What is the value of a+b?

• Circle Packing [Li, 01/22/2001]
  If circles packed in a 100 by 100 square are repacked so that the centers of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?

• New School Lockers [Lopez, 01/28/2001]
  Which locker was touched the most?

• How Many Handshakes? [Kathy, 01/29/2001]
  There are 40 people in a room. They shake each other's hands once and only once. How many handshakes are there altogether?

• The Predetermined Sum Puzzle [Tanya, 02/02/2001]
  I pick 5 digits, and write them down. My friend tells me a sum. Then I pick 5 more digits, he picks 5, I pick 5, and he picks 5. The sum he told me is the sum of all 5 lines. How did he know what it would be?

• Sums of Consecutive Integers [Kasey, 02/04/2001]
  What numbers can be expressed as the sum of a string of consecutive positive integers?

• 10-Digit Number Puzzle [Ihsan, 02/10/2001]
  How many possibilities are there for the 10-digit number abcdefghij if all of its digits are different and it is evenly divisible by 11111?

• Millionth Digit of the Counting Numbers [Bukovich, 02/26/2001]
  A number is formed by writing the counting numbers in order: 123456789101112131415... What is the one millionth digit in this number?

• Stair Patterns [Aghajani, 02/27/2001]
  The 1st step is made with 4 matches, the 2nd with 10 matches, the 3rd with 18, the fourth with 28. How many matches would be needed to build 6, 10, and 50 steps?

• A Practical Use for the Orthocenter [Hodel, 03/07/2001]
  Does the orthocenter of a triangle have any practical uses?

• Tracing a Figure Without Lifting Your Pencil [Kerri, 03/09/2001]
  Is there a simple way to quickly tell whether a figure can be traced without lifting your pencil?

• The 'First to 100' Game [Shanthi, 03/12/2001]
  Two players take turns choosing any number from 1-10, keeping a running sum of all the numbers. The first player to make this sum exactly 100 is the winner. Is there a surefire way to win this game?

• Coins in Change under $1 [Floyd, 03/13/2001]
  Is there a formula or equation for determining the smallest number of coins a person could receive when given change less than $1.00?

• 36 Sums, Blank Dice [Kim, 03/15/2001]
  You have two blank, six-sided dice, and you can put any numbers on them. The 12 numbers you choose should allow you to make the sums from 1-36...

• Pascal's Triangle Game [Stephen, 03/23/2001]
  How could I make a game using Pascal's triangle?

• Digit Reversal Trick Explained [Kouraklis, 03/23/2001]
  Take a 3-digit number and subtract its reverse. Then, take the result and add its reverse. Why is the answer is always 1089, no matter what the initial numbers were?

• Tic-Tac-Toe on a Torus [Joe, 03/29/2001]
  Can you make a tic-tac-toe game that won't end in a tie?

• Formula for the Day of the Month [Valadez, 04/05/2001]
  I have read the Dr. Math FAQ on finding the day of the week from the date. How do you get the part of the equation that deals with the month?

• Mangoes at the Gates [Dickerson, 04/06/2001]
  To pick some mangoes from a tree inside seven walls with seven guards, you tell each guard that you'll give him half of the mangos you have, but he must give you back one mango. What's the minimum number of mangos you must pick to have at least one mango left?

• Algebra Puzzle [Matias, 04/09/2001]
  If x+y+z = 1 and x^2 + y^2 + z^2 = 2 and x^3 + y^3 + z^3 = 3, what does x^4 + y^4 + z^4 equal?

• Rubik's Cube Combinations [Glapa, 04/11/2001]
  I read that a rubics cube has 4 quintillion different possible combinations. Is this number correct? How can I calculate this value on my own?

• Even-Numbered Magic Squares [David, 04/30/2001]
  How can I construct magic squares that work for even numbers?

• Counting Rectangles [Calabrese, 05/23/2001]
  How can I find the number of different rectangles in a square grid containing "c" columns and "r" rows?

• Stairs on an Escalator [Dario, 05/21/2001]
  A woman walks 10 steps down on a downward-moving escalator to reach the bottom. As she reaches the bottom, she runs back up the same escalator at a speed 5 times that which she walked down, covering 25 steps in reaching the top. How many steps are visible on the escalator when it is still?

• Crossing the Desert [Lefebvre, 05/22/2001]
  A truck gets one mile per gallon, and can hold 400 gallons at a time. How much is the minimum amount to cross a 1000-mile desert?

• Difference of Two Cubes [Jackie, 05/24/2001]
  The difference of two cubes is 56,765. What two positive integers satisfy this condition?

• Making Change for a Dollar [Kathy, 05/29/2001]
  What is the smallest number of coins you CANNOT make change with?

• Doubling Pennies for a Year [Epperson, 06/03/2001]
  How many pennies will we have at the end of 365 days if we begin on Januany 1 and double our money each day?

• Exchanging Seats in a Boat [Beth, 06/08/2001]
  Ten women are fishing in a long, narrow boat. One seat in the center of the boat is empty. The five women in the front of the boat want to change seats with the five women in the back of the boat...

• 30th of the Month [Selim, 06/18/2001]
  What day does the 30th of the month most often fall on?

• 19 Apple Trees [Johnson, 06/29/2001]
  You have 19 apple trees. How could you place them in 9 rows of 5?

• Three Hands on a Clock [Lucas, 07/03/2001]
  At what time after 12:00, to the fraction of a second, are the three hands on a clock on top of each other?

• 300 Foul Shots [Roger, 07/11/2001]
  A basketball player shoots 100 foul shots on a given day, and increases the number he shoots by 10 per day...

• Make $5 Using One of Each Coin [Steve, 07/07/2001]
  You have 100 coins: pennies, nickels, dimes, quarters, and half dollars. Use at least one of each to add up to $5.00.

• Unit Fractions Summing to 1 [Pamela, 07/15/2001]
  Find seven different unit fractions whose sum is 1.

• Coffee or Tea? [Traylor, 07/09/2001]
  Is there more coffee in the tea, or more tea in the coffee, or are they the same?

• Grid Game [Chad, 07/20/2001]
  This game for two players is played on a rectangular grid with a fixed number of rows and columns. Play begins in the bottom left-hand square...

• Minimum Number of Trips [Barbara, 07/01/2001]
  A fully laden lorry can carry fuel and supplies for a trip into the desert of up to 400 miles... How many trips would be needed to penetrate 600 miles and back?

• Largest 7-Digit Number [Patrick, 07/27/2001]
  Work out the largest 7-digit number you can applying two rules: every digit in the number must be able to be divided into the number, and no digit can be repeated.

• Four Dogs Running [Devon, 08/08/2001]
  Four dogs are at four corners of a field. Each dog chases the dog to its right; all four run at the same speed and no acceleration is assumed. Where will they meet, and how long and how far will they have run when they meet?

• 12345679 Puzzle - The Missing Eight [Michelle, 08/17/2001]
  Start with 12345679 and pick a number...

• 174 Game [Zhongwanting, 08/16/2001]
  Players announce numbers (1-8) in turn. The judge adds the numbers they announce. If the sum becomes 174 or more, that player wins. In order to win the game, which number should be given first?

• Birthday Calendar Puzzle [Nancy, 08/29/2001]
  My question involves a game that I have played with my students for a long time, yet I am always unable to explain to them why the pattern works...

• How Many Pencils? [Thomas, 09/05/2001]
  How many pencils does Al have if all of them are blue except 2, all of them are yellow except 2, and all of them are red except 2?

• Three Fractions [Kathleen, 09/06/2001]
  Three fractions together add up to one. Place the nine digits 1-9 in the fractions to make the equation a/bc + d/ef + g/hi = 1 correct.

• Calendar Puzzle [Bob, 09/09/2001]
  Take a calendar with five weeks, choose only one day out of each week, and write the date of each day. Then add up all the dates. How can you know the total of all the dates without looking at the calendar?

• Largest Magic Square Ever Known [Jayson, 09/18/2001]
  What is the largest magic square ever constructed?

• Milk Bottle Puzzle [Clare, 09/24/2001]
  Given 18 milk bottles and a milk crate 6 holes wide by 4 holes deep, put an even number of bottles into every row and column.

• The Hundred Fowls [Yana, 09/29/2001]
  If a rooster is worth five coins, a hen three coins, and three chickens together are worth one coin, how many roosters, hens, and chickens totaling 100 can be bought for 100 coins?

• Sums Divisible by 11 [Chris, 10/10/2001]
  Why is the sum of a number with an even number of digits and that same number written in reverse always divisible by 11?

• Words Equal to a Dollar [Marc, 10/11/2001]
  I need one-dollar words: a = 1, b = 2, c = 3...z = 26. I would like a list of words that equal 100.

• Clock Hands Diametrically Opposite [Jonathan, 10/10/2001]
  At what time between two and three o'clock are the hands of a clock diametrically opposite?

• Find Pairs of Positive Integers [Mike, 10/15/2001]
  Find pairs of positive integers whose greatest common factor is 1 and whose sum is 2000.

• Minimum Set of Weights Puzzle [Jhonen, 10/18/2001]
  What is the minimum number of weights needed for a scale that can weigh objects from 1-100 pounds, inclusive, at one-pound increments?

• Sum of First Four Digits Equals Units Digit [James, 10/20/2001]
  How many even five-digit numbers have the property that the sum of the first four digits is the units digit?

• Line Drawn through Lines Puzzle [Lauren, 10/18/2001]
  Given a box made up of 16 lines, with two rectangles above and three squares below, draw a line through each line without crossing any line twice.

• World War II Window Blackout [Heron, 10/21/2001]
  Mr. Brown had a square window 120cm x 120cm, but the only material he could find was a sheet of plywood 160cm x 90cm; same area, different shape. He drew some lines and cut out just two congruent shapes, which he joined to make a square of the correct size. How did he do it?

• 121, 111211, 311221 Puzzle [Joey, 10/23/2001]
  121, 111211, 311221 - what's the next number?

• Four 4's Puzzle [Ashley, 10/24/2001]
  How can you get 73 by using 4 fours and any mathematical equation?

• Product and Sum of Digits = Number [Meghan, 10/24/2001]
  How many two-digit numbers exist such that when the products of their digits are added to the sums of their digits, the result is equal to the original two-digit number?

• 2^4 = 16 AND 4^2 = 16 [Yvonne, 10/29/2001]
  Can you think of any other pair of unequal numbers that share the same relation as 2 and 4 in the above example? What was your strategy?

• Scoring System Problem [Kate, 10/28/2001]
  What is the highest score that is impossible to make?

• Ages 27-30 Puzzle [Jarrett, 11/06/2001]
  Alan was 27 years old the day before yesterday. Next year he will be 30. How is this possible?

• Non-negative Integers [Jannet, 11/15/2001]
  How many nonnegative integers consisting of 1-3 digits are divisible by 5? How many nonnegative integers consisting of 1-3 different digits are divisible by 5?

• Jack is Older than Jill [Danielle, 11/16/2001]
  If you reverse the digits in Jack's age, you get Jill's age. The sum of their ages equals 11 times the difference between them. Jack is older than Jill. What are their ages?

• Fibonacci Riddle [Daniel, 11/21/2001]
  We can cut an 8x8 square with an area of 64 into four pieces and reassemble to get a 5x13 rectangle with an area of 65. Where does the extra 1x1 square come from?

• Monkeys, Coconuts, and Seven Piles [Mike, 11/29/2001]
  Seven monkeys spend the day gathering coconuts. As night falls, they gather all the coconuts into one pile and agree to divide them up evenly in the morning. At 12:00pm one monkey gets up and divides the pile of coconuts into seven piles with one left over...

• TURKEYS puzzle [Donna, 11/28/2001]
  Count the number of ways you can trace the word TURKEYS in the triangular array. You may only move to one of the two letters directly below the letter you are on.

• Who Got Engaged to Whom? [Alina, 11/27/2001]
  Dorothy, Jean, Virginia, Bill, Jim, and Tom became engaged to one another. Who got engaged to whom?

• How Many People Went on the Cruise? [Jessica, 12/03/2001]
  At the end of a special cruise, the employees could not remember the total number of people who were on board. However, they had the following data from the passenger list: 520 European females...

• Minesweeper Puzzle [Jonathon, 10/24/2001]
  For the general case of an MxM board with N bombs, can you find the maximum value of the sum of all the numbers that are not bombs?

• Laying Eggs Better by Half [Kenneth, 12/05/2001]
  If a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half?

• Extraordinary Social Security Number [Elle, 12/05/2001]
  The number's nine digits contain all the digits from 1 to 9. When read from left to right the first two digits form a number divisible by two, the first three digits form a number divisible by three...

• 3 Digits Plus 3 Digits [Jake, 12/09/2001]
  Use the digits 1 to 9 only once in a sum that must be a three-digit number plus another three-digit number to equal another three-digit number. Each digit can only be used once, but all must be used.

• DEFABC Equals 6(ABCDEF) [Vincent, 12/10/2001]
  Let abcdef be a 6-digit integer such that defabc is 6 times the value of abcdef. Find the value of a + b + c + d + e + f.

• What Two Numbers? [Jessica, 01/05/2002]
  What two numbers, neither of them containing zeros, can be multiplied together to make 5,000,000,000?

• Find the Pattern, Complete the Combinations [Tracy, 01/13/2002]
  Find the pattern: 3*4=5, 8*4=0, 3*7=2, 1*2=9, and use it to complete the combinations: 5*5=?, 4*4=?, 5*7=?

• Headscratch Letter Puzzle [Ting, 01/25/2002]
  Use the numbers 0 to 9 for each letter once: G*B=HA, D*E=E, I*C=C, H* A=DE, F*J=GJ.

• Numbers with 5 Factors [Kyle, 02/06/2002]
  I know that 16 has 5 factors (1,2,4,8,16). What other two numbers might have 5 factors?

• Rectangles on a Chessboard [Dave, 02/09/2002]
  How many rectangles are there on a chessboard?

• Make 7,7,3,3 into 24 Using + - * and / [Jeremy, 02/12/2002]
  Make the numbers 7,7,3,3 equal 24 using the operations addition, subtraction, multiplication, and division.

• Pascal Calendar Program [Danilo, 02/12/2002]
  Holiday homework: make a program in Pascal that with a date of our choice give us the day of the week.

• Multiplying/Adding Fractions Gives Same Answer [Ryan, 03/01/2002]
  Find two fractions which, when multiplied and added, give the same answer.

• McNuggets [Roxanne, 03/10/2002]
  At one McDonald's location, McNuggets come in boxes of 6, 9, and 20. What would be the largest number of McNuggets that you could not buy?

• Where is the Arsenic? [Shae, 03/12/2002]
  You place six jars (right to left: coffee, arsenic, and sugar on the top shelf; snuff, tea, and salt on the bottom shelf)...

• Rational Number and its Reciprocal [Nelson, 03/14/2002]
  A rational number greater than one and its reciprocal have a sum of 2 1/6. What is this number? Express your answer as an improper fraction in lowest terms.

• Tumbling Dice by Robert Abbott [Jennifer, 03/17/2002]
  The center square is both the start and the goal: to solve the maze, you must move the die off the center square, then find a way to move it back onto that square...

• Magic Wheel [GB, 03/20/2002]
  Given a wheel with 16 spokes and a hub, enter the whole numbers 1-17 in the hub and at the end of spokes. The sums of the 3 numbers along the spokes must be equal.

• The Vicar and the Curate (Ages of Three People) [Jason, 03/20/2002]
  The product of the ages of three people is 2450 and the sum is twice the age of the curate. How old are the three people?

• U.S. and European Sock Sizes [Nomi, 03/23/2002]
  Which expression could be used to convert European size to U.S. size?

• ABCDC - BEAAC = BADAD [Arthur, 03/25/2002]
  What to the letters stand for if D = 0?

• The 22 Puzzle [Sam, 03/12/2002]
  Choose three different digits from 1-9, make all the 2-digit numbers you can from these 3 digits... why is the answer always 22?