Subj:     Math4b - Puzzles And Problems
                 (Includes 48 jokes and articles, 17 1014,30,cf,vYT3,23)

          Click "Here" for MATH4b-Supp
          Click "Here" for MATH4b-Supp2

..........Click Math4A for more puzzles
..........Click Math4C for more puzzles
......and Click Math4D for more puzzles


Compass from
Best Animation
Includes the following:  Math Prob. - Longer Line? (S614c in Supp)
.........................Math Prob. - An Addition Problem (S588 in Supp2)
.........................Math Prob. - Archery Puzzle (S588 in Supp2)
.........................Math Prob. - Trading In The Philippines (S587 in Supp2)
.........................Math Prob. - Socks In A Drawer (S586 in Supp2)
.........................Math Prob. - Problems of History (S585 in Supp2)
.........................Math Prob. - Walking From The Train Station (S583 in Supp2)
.........................Math Prob. - Four Digit Number #2 (S579b in Supp2)
.........................Math Prob. - Brothers And Sisters (S577b in Supp2)
.........................Math Prob. - Find Two Numbers (S573 in Supp2)
.........................Math Prob. - 100 Men (S570 in Supp2)
.........................Math Prob. - Cat Equation (S564a in Supp2)
.........................Math Prob. - Odd-One-Out (S556 in Supp2)
.........................Math Prob. - Four Digit Number (S553c in Supp2)
.........................MATH PROB. - A Length Of Rope (S547c in Supp2)
.........................MATH PROB. - Find Two Numbers (S545 in Supp2)
.........................MATH PROB. - Find Three Digits (S541c in Supp2)
.........................MATH PROB. - Two Hourglasses And An Egg (S538c in Supp2)
.........................Math Prob. - Average Speed (S537 in Supp2)
.........................Math Prob. - Cookies And Milk (S537 in Supp2)
.........................Math Prob. - The Groom's Age (S534 in Supp2)
.........................Math Prob. - Numbers On A Dice (S534c in Supp2)
.........................Math Prob. - What Is The Next Number? (S533c in Supp2)
.........................Math Prob. - Five Digit Number (S532c in Supp2)
.........................
.........................MATH PROB. - Semicircle In A Triangle (S492 in Supp)
.........................MATH PROB. - Meat Purchase (S490 in Supp)
.........................Math Prob. - Three Women's Ages (S531c in Supp)
.........................Math Prob. - Crab Weights (S528 in Supp)
.........................Math Prob. - Three Sister's Ages (S523c in Supp)
.........................Math Prob. - Maria's Age (S521c in Supp)
.........................Math Prob. - Two Clocks (S519 in Supp)
.........................Math Prob. - Old Man Wrinkle's Age (S517 in Supp)
.........................Math Prob. - Marriage Knot (S516 in Supp)
.........................Math Prob. - Three Beggars (S516c in Supp)
.........................Math Prob. - Four Balls In A Hat (S514c in Supp)
.........................Math Prob. - Fruit Stand Weights (S512c in Supp)
.........................Math Prob. - Cost of War (S511 in Supp)
.........................MATH PROB. - Karen's Age (S507 in Supp)
.........................MATH PROB. - What Is The Next Number (S507c in Supp)
.........................MATH PROB. - A String Of Ones (S503 in Supp)
.........................MATH PROB. - Word Arithmetic (S498 in Supp)
.........................MATH PROB. - Eve Did Talk (S496c in Supp)
.........................MATH PROB. - What Number Comes Next? (S495c in Supp)
.........................MATH PROB. - The Father's Will (S495 in Supp)
.........................MATH PROB. - Find The Ants Shortest Route (S495c in Supp)
.........................MATH PROB. - 123456789 = 100 (S494 in Supp)
.........................MATH PROB. - Number Riddle (S493c in Supp)
.........................
.........................The Argyle Sweater - Cartoon (S1014)
.........................MATH PROB. - Three Numeric Palindromes (S493)
.........................MATH PROB. - The Slug And The Snail (S488)
.........................MATH PROB. - Find Ratio Of X To Z (S487c)
.........................MATH PROB. - A Clock Puzzle (S486, S601)
.........................MATH PROB. - The Desert (S485)
.........................MATH PROB. - Trolls And Cakes (S480c)
.........................MATH PROB. - Four 4s (S476)
.........................MATH PROB. - Horse race (S476c)
.........................MATH PROB. - Three Powers (S475)
.........................MATH PROB. - Solve for X (S474)
.........................MATH PROB. - Hexagon In A Circle (S473)
.........................MATH PROB. - Square Inscribed In A Triangle (S473c)
.........................MATH PROB. - Rope Around The Earth (S472)
.........................MATH PROB. - Band Around The Earth (S472c)
.........................MATH PROB. - Car Journey (S471)
.........................MATH PROB. - Difference Of Powers (S470b)
.........................MATH PROB. - Cyclic Hexagon (S469)
.........................MATH PROB. - Cubic Resistor (S469b)
.........................MATH PROB. - Five Marbles (S468b)
.........................MATH PROB. - Conway Sequence (S468)
.........................MATH PROB. - Nine Trees and Ten Rows (S462b)
.........................
.........................LOGIC PROB. - Pink, White, And Blue (S582 in Supp2)
.........................LOGIC PROB. - Figure Analogy (S580 in Supp2)
.........................LOGIC PROB. - Cube In Perspective (S580 in Supp2)
.........................LOGIC PROB. - Which Figure Does Not Belong (S577 in Supp2)
.........................LOGIC PROB. - Missing Numbers (S561 in Supp2)
.........................LOGIC PROB. - Three Names (S559 in Supp2)
.........................LOGIC PROB. - The Right Cube (S548c in Supp2)
.........................LOGIC PROB. - Three Playing Cards (S544 in Supp2)
.........................LOGIC PROB. - 15 Delegates (S541 in Supp2)
.........................LOGIC PROB. - Which Diagram Is Different #2 (S538 in Supp2)
.........................LOGIC PROB. - What Is Next In The Sequence (S536 in Supp2)
.........................LOGIC PROB. - Two Towns And A Railroad (S536c in Supp2)
.........................LOGIC PROB. - Liars And Truthtellers (S535c in Supp2)
.........................LOGIC PROB. - Which Diagram Is Different (S535 in Supp2)
.........................
.........................LOGIC PROB. - Is this true? (S531 in Supp)
.........................LOGIC PROB. - Frog Leap (S530c in Supp)
.........................LOGIC PROB. - Frog Leap II (S624b in Supp)
.........................LOGIC PROB. - Complete The Analogy (S530 in Supp)
.........................LOGIC PROB. - Four-Digit Number (S515c in Supp)
.........................LOGIC PROB. - Crossing Time (S506 in Supp)
.........................LOGIC PROB. - How Many Circles? (S506c in Supp)
.........................LOGIC PROB. - Consecutive Elements (S505c in Supp)
.........................LOGIC PROB. - HAT's Off (S498c in Supp)
.........................LOGIC PROB. - Figure Logic 1 (S496 in Supp)
.........................LOGIC PROB. - Figure Logic 2 (S497c in Supp)
.........................
.........................LOGIC PROB. - Cards And Numbers Problem (S491)
.........................LOGIC PROB. - 3D Logic (S490c)
.........................LOGIC PROB. - Priests And Devils (S489c)
.........................LOGIC PROB. - Alien Mutation (S488c)
.........................LOGIC PROB. - Letters To Numbers (S485c)
.........................LOGIC PROB. - IQ Test (S477c)
.........................LOGIC PROB. - Sequence Of Six Numbers II (S474c)
.........................LOGIC PROB. - Sequence Of Six Numbers (S471b)
.........................LOGIC PROB. - Two Pool Balls (S467b)
.........................LOGIC PROB. - Birthday Paradox (S467)
.........................LOGIC PROB. - Three children (S465)
.........................
.........................Puzzle - Puzzling Scales By Sam Loyd (S585 in Supp2)
.........................Puzzle - Count The Squares (S578 in Supp2)
.........................Puzzle - Three Utilities (S578 in Supp2)
.........................Puzzle - Missing Number (S576 in Supp2)
.........................Puzzle - Making Bracelets (S558 in Supp2)
.........................Puzzle - Count The Triangles II (S545c in Supp2)
.........................Puzzle - Distributing A Man's Legacy (S533 in Supp2)
.........................Puzzle - Remembering Pi (S532 in Supp2)
.........................
.........................Puzzle - Count The Triangles (S525 in Supp)
.........................Puzzle - 5 By 5 Magic Square (S526c in Supp)
.........................Puzzle - Two Ropes (S525 in Supp)
.........................Puzzle - How Many Squares (S524c in Supp)
.........................Puzzle - The Elder Twin (S515 in Supp)
.........................Puzzle - Artist's Puzzle (S511c in Supp)
.........................Puzzle - Coal, Carrot, And A Scarf (S509c in Supp)
.........................Puzzle - Rotating Coin Paradox (S504 in Supp)
.........................Puzzle - Map Coloring (S502c in Supp)
.........................Puzzle - Square Puzzle (S500 in Supp)
.........................Puzzle - Draw Four Lines (S500c in Supp)
.........................Puzzle - Five Queens And Three Pawns (S497 in Supp)
.........................Puzzle - Magic Gopher (S492 in Supp)
.........................
.........................Puzzle - Penrose Rhombs (S486c)
.........................Puzzle - Mobius Chess (S484c)
.........................Puzzle - Water Puzzle, Three Glasses (S484)
.........................Puzzle - Red To Green (S483)
.........................Puzzle - Triangles In The Letter M (S482c)
.........................Puzzle - Figures And Words (S481)
.........................Puzzle - Ninteen Roses (S479c)
.........................Puzzle - Folded Cube (S479)
.........................Puzzle - Ten Roses (S478)
.........................Puzzle - Toroid's Missing Color (S478c)
.........................Puzzle - Seven Roses (S477)
.........................Puzzle - Apples Delivery (S475c)
.........................Puzzle - Wire Cuffs (S469b)
.........................Puzzle - Lewis Carroll's Pillow Problem (S462)
.........................Puzzle - Family Statistics (S462b)
 

The MATH1 file are nonmathematical math jokes
    MATH2 file are mathematical jokes
    Math3 file contains tests, and formulas
    Math4 file contains problems
    Math5 file contains quotes
    MATH6 file contains lymerics, short jokes, stories, and QA.

To see other type puzzles go to the following:
         Bottle Caps  -  (See whole file)
         BRAIN TEASERS-  (See whole file)
         ILLUSIONS    - 'Two triangles Problem'
......................-..(See whole file)
         Riddles file -  (See whole file)
         WORD PUZZLES -  (See whole file)
         TEST FACES   -  (See whole file)
============================================================Top
Subj:     The Argyle Sweater - Cartoon (S1014)
          Created by Scott Hilburn on 1/16/2010
 Source: http://www.gocomics.com/theargylesweater/2010/01/16
.
................
.
.
Top
Subj:     MATH PROB. - Three Numeric Palindromes (S493)
          © Copyright 2002, Jim Loy
 Source: https://www.algebra.com/algebra/homework/word/misc/
.........Miscellaneous_Word_Problems.faq.question.851668.html

 This is an original puzzle which I stumbled upon.  I have
 before me three numeric palindromes (numbers which read the
 same backwards and forwards, like 838).  The first is two
 digits long; the second is three digits, and when we add
 those two numbers together we get the third number which is
 four digits long. What are the three numbers?

 The solution can be found at the source above.

Top
Subj:     MATH PROB. - The Slug And The Snail (S488)
          From: QBrute on 5/27/2006
 Source: http://www.angelfire.com/empire/qbrute/puzzles.htm

 A slug and a snail decided to settle a long-standing argument
 as to who was the best sprinter. So they planned a race
 between two stones set a distance D cm apart.  Said the slug
 to the snail "Since I'm slimier than you, I intend to start
 T seconds before you". "In that case," said the snail, who
 was rather slow, "I'm going to give you X cm start".  It did
 not matter.  The slug, who could move at speed V cm/sec, was
 only half as fast as the snail.  The result was a dead heat,
 t seconds after the slug set off.  Now, D,t,T,V and X were
 all whole numbers from 1 to 10 inclusive, no two numbers
 being the same.  How long did it take the snail to reach the
 finish?

Top
Subj:     MATH PROB. - Find Ratio Of X To Z (S487c)
          From: LABLaughsRiddles on 5/16/2006

 X, Y, and Z satisfy:
 X - Y - Z = 0 and 2X + Y + 3Z = 0
 If Z is nonzero, what is the ratio of X to Z?
 
 
 To see the solution click

Top
Subj:     MATH PROB. - A Clock Puzzle (S486, S601)
          © Copyright 2000, Jim Loy
..........At: (Removed from jimloy.com)

 A well-known and simple puzzle is this: The hour and minute
 hands of a clock are superimposed at 12:00.  When will they
 next be superimposed (I don't mean lined up as they are at 6:00)?
 

 To view the solution, click  .

Top
Subj:     MATH PROB. - The Desert (S485)
          From: The Contest Center on 5/9/2006
 Source: http://www.contestcen.com/tough.htm

 Sir John must drive his jeep across the Kanahara Desert and
 reach Khartoun, some 2500 miles away.  The gas tank holds 15
 gallons, and the jeep can carry up to 10 jerry cans of
 gasoline each holding 5 gallons.  Gasoline can be poured
 from a can into the gas tank, or from one can into another
 without loss, but gasoline cannot be siphoned from the tank
 into a can.  It is safe to stash cans along the way and pick
 them up later.  There is a large supply of gasoline and jerry
 cans in the town where he is starting, but they are both very
 expensive.  The jeep gets 10 miles to the gallon.  How can he
 get there using the least amount of gasoline?

Top
Subj:     MATH PROB. - Trolls And Cakes (S480c)
          From: LABLaughs.com on 3/21/2006

 You are on your way to visit your Grandma, who lives at the
 end of the valley. It's her birthday, and you want to give
 her the cakes you've made.

 Between your house and her house, you have to cross 7 bridges,
 and as it goes in the land of make believe, there is a troll
 under every bridge! Each troll, quite rightly, insists that
 you pay a troll toll.  Before you can cross their bridge, you
 have to give them half of the cakes you are carrying, but as
 they are kind trolls, they each give you back a single cake.

 How many cakes do you have to leave home with to make sure
 that you arrive at Grandma's with exactly 2 cakes?

x
x
x
x
x
Scroll down for the answer
x
x
x
x
x
Here it comes
x
x
x
x
x
 

 2: At each bridge you are required to give half of your cakes,
 and you receive one back.  Which leaves you with 2 cakes after
 every bridge.

Top
Subj:     MATH PROB. - Four 4s (S476)
          From: Math Forum
 Source: http://mathforum.org/k12/k12puzzles/

 Using four 4's and any operations, try to write equations
 that have the numbers from 0 to 100 as the answer.

 Examples: 4/4 + 4 - 4 = 1
           4/4 + 4/4 = 2
           Square root of 4 + Square root of 4 - 4/4 = 3

Top
Subj:     MATH PROB. - Horse race (S476c)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle14.html

 In how many ways, counting ties, can eight horses cross the
 finishing line? (For example, two horses, A and B, can finish
 in three ways: A wins, B wins, A and B tie.)

 The solution can be found at the source above.

Top
Subj:     MATH PROB. - Three Powers (S475)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle10.html
 
 
Find all solutions of
, for integers x, y, and z.

     The solution can be found at the source above.

Top
Subj:     MATH PROB. - Solve for X (S474)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle09.html
 
Solve the equation 
= x.

     (All square roots are to be taken as positive.)

     The solution can be found at the source above.

Top
Subj:     MATH PROB. - Hexagon In A Circle (S473)
          From: William Wu of U. C. Berkeley on 2/1/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#hexagonInCircle

 A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed
 in a circle. Find the radius of the circle.

Top
Subj:     MATH PROB. - Square Inscribed In A Triangle (S473c)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle08.html

 A triangle has sides 10, 17, and 21.  A square is inscribed
 in the triangle.  One side of the square lies on the longest
 side of the triangle.  The other two vertices of the square
 touch the two shorter sides of the triangle.  What is the
 length of the side of the square?
.
..........
.
 The solution can be found at the source above.

Top
Subj:     MATH PROB. - Rope Around The Earth (S472)
          From: William Wu of U. C. Berkeley on 2/1/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#molinaUrns

 Assume the Earth is a perfect sphere of radius r and suppose
 a rope of zero elasticity is tied tightly around it. One meter
 is now added to the rope's length. If the rope is now pulled
 at one point as high as possible above the Earth's surface,
 what height will be reached?

Top
Subj:     MATH PROB. - Band Around The Earth (S472c)
          From my years of teaching

 Assume the Earth is a perfect sphere of radius r and suppose
 a band of zero elasticity is tied tightly around it. One meter
 is now added to the band's length. If the band is adjusted to
 even the increase in the radius everywhere, could a two inch
 mouse go between the band and the earth?

Top
Subj:     MATH PROB. - Car Journey (S471)
         From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle08.html

 A car travels downhill at 72 m.p.h. (miles per hour), on the
 level at 63 m.p.h., and uphill at only 56 m.p.h.  The car takes
 4 hours to travel from town A to town B.  The return trip takes
 4 hours and 40 minutes.  Find the distance between the two towns.

 The solution can be found at the source above.

Top
Subj:     MATH PROB. - Difference Of Powers (S470b)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle07.html

 Find all ordered pairs (a,b) of positive integers such that

. = 1.

 The solution can be found at the source above.

Top
Subj:     MATH PROB. - Cyclic Hexagon (S469)
          From: Nick's Mathematical Puzzles on 1/16/2006
 Source: http://www.qbyte.org/puzzles/puzzle07.html
 
 
A hexagon with
consecutive sides
of lengths 2, 2, 7,
7, 11, and 11 is
inscribed in a circle.
 
 

Find the radius of
the circle.
 
 

The solution can be
found at the source above.
 
 

 

Top
Subj:     MATH PROB. - Cubic Resistor (S469b)
          From: William Wu of U. C. Berkeley on 1/16/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#resistorCube

 Imagine a cube where each edge is a 1 ohm resistor. Find the
 resistance between opposite corners of the cube.

 There are many ways to solve this problem, but some ways are
 more clever than others.

Top
Subj:     MATH PROB. - Five Marbles (S468b)
          From: Nick's Mathematical Puzzles on 1/13/2006
 Source: http://www.qbyte.org/puzzles/puzzle04.html
.
Five marbles of various sizes are placed in a conical funnel.  Each marble is in contact with the adjacent marble(s).  Also, each marble is in contact all around the funnel wall.
 

The smallest marble has a radius of 8mm.  The largest marble has a radius of 18mm.  What is the radius of the middle marble?
 

The solution can be found at the source above.

Top
Subj:     MATH PROB. - Conway Sequence (S468)
          From: William Wu of U. C. Berkeley on 1/13/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#conwaySequence

What row of numbers comes next?

 1
 11
 21
 1211
 111221
 312211
 13112221

-----------------------------------------------------------

 Note: Mathematician John Conway spent considerable time
       studying this sequence.
 
 To see Abe's excellent solution click on

Top
Subj:     MATH PROB. - Nine Trees and Ten Rows (S462b)
          From: William Wu of U. C. Berkeley on 1/7/2006
         At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#treesForWillywutang

 So, Willywutang has (somehow) managed to get himself a nice
 big mansion.  The mansion has a nice huge yard in front.
 However, the yard is completely flat and boring, so Willy
 decides it'd look nice with a few trees in front.  So, he
 has a landscaper come in to put in some trees.  Being the
 puzzlemeister that he is, Willy decides to give the land-
 scaper a riddle: Plant 9 trees in the yard, so that there
 are 10 rows of three trees each. Help the poor landscaper
 decide how to place the trees.

 I have found nine trees and eight rows, and nine trees and
 nine rows, but I am stumped with nine trees and ten row.
 Maybe one of you will solve it.

 Anon Jr. found the solution on the internet.  You can view
 it at  .

Top
Subj:     LOGIC PROB. - Cards And Numbers Problem
          From: Norfolk Academy (S491) on 6/18/2006
 Source: (Removed from norfacad.pvt.k12.va.us)

 This is a very simple logic problem.  See how much you
 remember by clicking 'HERE'.

Top
Subj:     LOGIC PROB. - 3D Logic (S490c,d)
          From: FreeWorldGroup.com on 6/11/2006
 Source: http://www.freeworldgroup.com/games4/gameindex/3dlogicgame.html

 Link every pair of like-colored markers to complete a cube.
 You can play this logic game by clicking 'HERE'.

Top
Subj:   LOGIC PROB. - Priests And Devils (S489c,d)
          From: FreeWorldGroup.com on 6/6/2006
 Source: http://www.freeworldgroup.com/games3/gameindex/priestsanddemons.html

 Help the Priests and Devils cross the river. But be warned!
 If the Priests are out numbered by the Devils on either side
 of the river, they will be killed! You can play this logic
 game by clicking 'HERE'.

Top
Subj:     LOGIC PROB. - Alien Mutation (S488c)
          From: QBrute on 5/27/2006
 Source: http://www.angelfire.com/empire/qbrute/puzzles.htm

 Can you determine what each of the 12 mutation chambers does.
 You can try this easy puzzle by clicking 'HERE'.

Top
Subj:     LOGIC PROB. - Letters To Numbers (S485c)
          From: MathsIsFun.com on 5/9/2006
 Source: http://www.mathsisfun.com/twelve.html

...............................TWO
..........................+  THREE
.............................SEVEN
..........................--------
............................TWELVE

 Put numbers where the letters are, and makes the sum be true.

Top
Subj:     LOGIC PROB. - IQ Test (S477c)
          From: HighIQSociety on 3/8/2006
 Source: http://www.highiqsociety.org/iq_tests/

 Have you ever wondered what your IQ score was?  Go to the
 above web site, click on the top button (shown to the right)
 and answer their 36 questions, and you will be shown a pretty
 good estimate of your IQ.

Top
Subj:     LOGIC PROB. - Sequence Of Six Numbers II (S474bc)
          From: Anon Jr. on 1/23/2006

 What are the next four numbers in the sequence of
 1, 2, 4, 5, 7, 8, 11, 12, 15, 16 ?

Top
Subj:     LOGIC PROB. - Sequence Of Six Numbers (S471b)
          From: Anon Jr. on 1/23/2006

 What are the next four numbers in the sequence of
 1, 2, 3, 7, 15, 16 ?

 Junior had to give me two hints before I could find them.

 To view the solution, click .

Top
Subj:     LOGIC PROB. - Two Pool Balls (S467b)
          From: Nick's Mathematical Puzzles on 1/7/2006
 Source: http://www.qbyte.org/puzzles/puzzle03.html

 A cloth bag contains a pool ball, which is known to be a spot.
 A second pool ball is chosen at random in such a way that it
 is equally likely to be a spot or a stripe.  The ball is added
 to the bag, the bag is shaken, and a ball is drawn at random.
 This ball proves to be a spot.  What is the probability that
 the ball remaining in the bag is also a spot?

Top
Subj:     LOGIC PROB. - Birthday Paradox (S467)
          From: William Wu of U. C. Berkeley on 1/1/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#birthdayParadox

 There are N people in one room. How big does N have to be
 until the probability that at least two people in the room
 have the same birthday is greater than 50 percent? (Same
 birthday means same month and day, but not necessarily same
 year.)

 Note: This problem is not really a paradox, but it is given
 this label because the answer is hard to believe.

Top
Subj:     LOGIC PROB. - Three children (S465)
          From: Nick's Mathematical Puzzles on 12/17/2005
 Source: http://www.qbyte.org/puzzles/puzzle02.html

 On the first day of a new job, a colleague invites you around
 for a barbecue.  As the two of you arrive at his home, a young
 boy throws open the door to welcome his father.  "My other two
 kids will be home soon!" remarks your colleague.

 Waiting in the kitchen while your colleague gets some drinks
 from the basement, you notice a letter from the principal of
 the local school tacked to the noticeboard.  "Dear Parents,"
 it begins, "This is the time of year when I write to all
 parents, such as yourselves, who have a girl or girls in the
 school, asking you to volunteer your time to help the girls'
 soccer team."  "Hmmm," you think to yourself, "clearly they
 have at least one of each!"

 This, of course, leaves two possibilities: two boys and a girl,
 or two girls and a boy.  Are these two possibilities equally
 likely, or is one more likely than the other?

Top
Subj:     Puzzle - Penrose Rhombs (S486c)
          From: University of Idaho on 5/13/2006
 Source: (Removed from cs.uidaho.edu)

 These two rhombs were drawn by the British physicist Roger
 Penrose, hence they are called Penrose Rhombs.  Try to
 tile a plane with these two rhombs.  There are only two rules:
 1. Colors must match at the edges
 2. Leave no gaps
 For a set of tiles to work this puzzle, click 'HERE'.

Top
Subj:     Puzzle - Mobius Chess (S484c)
          From: Perplexus Dot Info on 4/30/2006
 Source: http://perplexus.info/show.php?pid=4050?op=sol

 This chess board is on a Mobius strip.  Can you find the
 checkmate.  You can view the puzzle by clicking 'HERE'.

Top
Subj:     Puzzle - Water Puzzle, Three Glasses (S484)
          From: Interactive Mathematics on 4/30/2006
 Source: http://www.cut-the-knot.org/water.shtml
Picture from Yahoo Images

 There are three glasses on the table - 3, 5, and 8 oz.  The
 first two are empty, the last contains 8 oz of water. By
 pouring water from one glass to another make at least one
 of them contain exactly 4 oz of water.

 You can solve this cute, interactive math puzzle
 by clicking 'HERE'.

Top
Subj:     Puzzle - Red To Green (S483)
          From: HighIQSociety on 4/8/2006
 Source: http://www.highiqsociety.org/puzzles/puzzle3_3.php

 What is the smallest number of red balls that must be moved
 to transform the red triangle into the green triangle?
.
..........
..
 To see the solution click on

Top
Subj:     Puzzle - Triangles In The Letter M (S482c)
          From: MathForum on 3/19/2006
 Source: http://mathforum.org/k12/k12puzzles/mpuzzle.html

 Can you construct nine triangles by drawing three straight
 lines through this capital M?
.
....................
..
 
 To see the MathForum's solution click on

Top
Subj:     Puzzle - Figures And Words (S481)
          From: HighIQSociety  on 4/8/2006
 Source: http://www.highiqsociety.org/puzzles/puzzle3_2.php

 Can you determine the relationships between the figures and
 the words to find the solutions to the two unknowns?  You
 can see this puzzle by clicking 'HERE'.

Top
Subj:     Puzzle - Ninteen Roses (S479c)
          From: MathForum on 3/8/2006
 Source: http://mathforum.org/k12/k12puzzles/rosebush.puzzle3.html

 A gardener laying out a bed of roses planted 19 rosebushes in
 9 straight lines with 5 bushes in each line.  How did she do it?

 The solution can be found at the source above.

Top
Subj:     Puzzle - Folded Cube (S479)
          From: HighIQSociety  on 3/8/2006
 Source: http://www.highiqsociety.org/puzzles/puzzle2_2.php

 Can you figure out when the six sides are folded into a cube,
 what it will look like?  You can try by clicking 'HERE'.

Top
Subj:     Puzzle - Ten Roses (S478)
          From: MathForum on 3/8/2006
 Source: http://mathforum.org/k12/k12puzzles/rosebush.puzzle2.html

 A gardener laying out a bed of roses planted ten rose bushes
 in five straight lines with four bushes in each line.  How
 did he do it?

 The solution can be found at the source above.

Top
Subj:     Puzzle - Toroid's Missing Color (S478c)
          From: HighIQSociety on 3/8/2006
 Source: http://www.highiqsociety.org/puzzles/puzzle1_2.php

 You can view this easy, but beautiful puzzle by clicking 'HERE'.

Top
Subj:     Puzzle - Seven Roses (S477)
          From: MathForum on 3/8/2006
 Source: http://mathforum.org/k12/k12puzzles/rosebush.puzzle1.html

 A gardener laying out a bed of roses finds that she can
 plant 7 rosebushes so that they form 6 straight lines
 with 3 rosebushes in each line.  How is this possible?

 The solution can be found at the source above.

Top
Subj:     Puzzle - Apples Delivery (S475c)

 Source: http://www.math.utah.edu/~cherk/puzzles.html

 The distance between the towns A and B is 1000 miles.  There
 is 3000 apples in A, and the apples have to be delivered to B.
 The available car can take 1000 apples at most. The car driver
 has developed an addiction to apples: when he has apples aboard
 he eats 1 apple with each mile made.  Figure out the strategy
 that yields the largest amount of apples to be delivered to B.
 Generalize the strategy for an arbitrary amount of apples.
 
 
 To see Jacks's solution click on

Top
Subj:     Puzzle - Wire Cuffs (S470)
          From: William Wu of U. C. Berkeley on 1/16/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#wirecuffs
 
In a cliche effort to illustrate the importance of teamwork-
oriented problem solving, the Boss has chained Dilbert to Carol The Secretary via wire wrapped around their wrists, as shown in the right snapshot:
The goal is for Dilbert and Carol to unlink themselves
from each other; considering what a horrible woman Carol
is, Dilbert wouldn't have it any other way. The wire is
unbreakable, and as much as Dilbert would like to saw off
Carol's limbs, that's against company policy.  How can
Dilbert and Carol get away from each other?

Top
Subj:     Puzzle - Lewis Carroll's Pillow Problem (S462)
          From: Interactive Mathematics Miscellany and Puzzles
          on 11/28/2005
 Source: http://www.cut-the-knot.org/carroll.shtml

 This problem is cited by M. Gardner in his Mathematical
 Circus and also Gardner's Workout.

 A bag contains a counter, known to be either white or black.
 A white counter is put in, the bag is shaken, and a counter
 is drawn out, which proves to be white. What is now the chance
 of drawing a white counter?

 Lewis Carroll offers two solutions with proofs leading to
 the answers of 1/2 and 2/3.  If you can't decide on the
 correct answer, click on the source above.

Top
Subj:     Puzzle - Family Statistics (S462b)
          From: Interactive Mathematics Miscellany and Puzzles
          on 11/28/2005
 Source: http://www.cut-the-knot.org/Curriculum
........./Probability/FamilyStats.shtml

          "Do men have more sisters than women?"

 The answer surprised me to the point that I included the
 problem on my Sunday Morning Laughs.  If you are not happy
 with your answer, click on the source above.

                            \\\//
                           -(o o)-
========================oOO==(_)==OOo======================
.............................From RFSlick on 6/11/05
.