Subj:
Math4b  Puzzles And Problems
(Includes 48 jokes and articles, 17 1014,30,cf,vYT3,23)
Click "Here" for MATH4bSupp
..........Click
Math4A
for more puzzles


Compass from Best Animation 
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 longstanding 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 
Subj:
MATH PROB.  A Clock Puzzle (S486, S601)
© Copyright 2000, Jim Loy ..........At: (Removed from jimloy.com) 
A wellknown 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)?
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 solution can be

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
.
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'.
Subj:
LOGIC PROB.  3D Logic (S490c,d)
From: FreeWorldGroup.com on 6/11/2006 
Link every pair of likecolored
markers to complete a cube.
You can play this logic game
by clicking 'HERE'.
Subj: LOGIC
PROB.  Priests And Devils (S489c,d)
From: FreeWorldGroup.com on 6/6/2006 
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'.
Subj:
LOGIC PROB.  Alien Mutation (S488c)
From: QBrute on 5/27/2006 
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.
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.
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?
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'.
Subj:
Puzzle  Mobius Chess (S484c)
From: Perplexus Dot Info on 4/30/2006 
This chess board is on a Mobius
strip. Can you find the
checkmate. You can view
the puzzle by clicking
'HERE'.
Subj:
Puzzle  Water Puzzle, Three Glasses (S484)
From: Interactive Mathematics on 4/30/2006 Source: http://www.cuttheknot.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 
Subj:
Puzzle  Figures And Words (S481)
From: HighIQSociety on 4/8/2006 
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'.
Subj:
Puzzle  Ninteen Roses (S479c)
From: MathForum on 3/8/2006 
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.
Subj:
Puzzle  Folded Cube (S479)
From: HighIQSociety on 3/8/2006 
Can you figure out when the six
sides are folded into a cube,
what it will look like?
You can try by clicking
'HERE'.
Subj:
Puzzle  Ten Roses (S478)
From: MathForum on 3/8/2006 
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.
Subj:
Puzzle  Toroid's Missing Color (S478c)
From: HighIQSociety on 3/8/2006 
You can view this easy, but beautiful puzzle by clicking 'HERE'.
Subj:
Puzzle  Seven Roses (S477)
From: MathForum on 3/8/2006 
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.cuttheknot.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.cuttheknot.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
.