Puzzles Archive
This is a list of the previous puzzles that have been sent out by
E-mail.
Don't forget to signup for "The MindBender" here.
To see the answer, click and hold your mouse button just to the right
of the red arrow 
and drag down. This will highlight
the answer and make it visible.
March 15, 1999
Cryptogram
Each letter stands for another. If you think D=K, for example, it
would equal K throughout the puzzle. The code for this Cryptogram and the
Mini-MindBender below are not the same.
Decode the following:
Cryptogram Clue: X equals G
NTR XGF CTQ YOPRONRL WSEXTRNNY CEW SQWYNYPRAF GWYOX TYW OQQLAR.
___________________________
Mini-MindBender for Kids
Easy Cryptogram
Each letter stands for another. If you think D=K, for example, it
would equal K throughout the puzzle. The code for this Cryptogram and the
MindBender above are not the same.
Decode the following:
Cryptogram Clue: X equals P
CLTSWA, MEW XRTXUW YZSBOLRT, UBDWO LSAMEZSQ MELM ZO QTLXW GULDBTWY.
A second clue, if desired, is below.
Second Cryptogram Clue: T equals R
___________________________
...Answer to MindBender
Cryptogram
This answer is best viewed in a mono-space font like Courier.
THE GUY WHO INVENTED SPAGHETTI WAS POSITIVELY USING HIS NOODLE.
This Cryptogram came from the Minneapolis Star Tribune newspaper.
___________________________
Answer to Mini-MindBender for Kids
Easy Cryptogram
This answer is best viewed in a mono-space font like Courier.
BARNEY, THE PURPLE DINOSAUR, LOVES ANYTHING THAT IS GRAPE FLAVORED.
March 22, 1999
MindBender
Cryptarithmetic Puzzle
This is a Cryptarithmetic puzzle. It represents a long-division problem,
where each digit has been replaced by a different letter. You are to
determine the digit that corresponds to each letter. When you are done,
arranging the letters in order from the letter corresponding to 0 up to the
letter corresponding to 9 will spell out a short English word or phrase.
.........ION
....+-------
PIP | GNEISS
......NMAR
......----
.......GPSS
.......GSOO
.......----
........NNNS
.........PIP
........----
.........OEM
Note: The divisor, dividend, and quotient are all English words.
___________________________
Mini-MindBender for Kids
Spaceball
Zork is looking for friends to play spaceball. His friends all live in his
solar system. Zork leaves his planet and flies 5 planets west to get Zeek.
Zeek lives on the first planet in the solar system. Then Zork flies east 8
planets to get Zook. From there he flies west 6 planets to find Zurk. Then he
flies east 9 planets for Zack. Zack lives on the last planet in the solar
system. How many planets are in Zork's solar system?
...Answer to MindBender
Cryptarithmetic
.........341
....+-------
636 | 217355
......1908
......----
.......2655
.......2544
.......----
........1115
.........636
........----
.........479
And the zero-to-nine word is ANGIOSPERM.
This MindBender came from:
http://www.cs.umbc.edu/cgi-bin/mayfield-hook/crypt
a web page that automatically generates Cryptarithmetic puzzles. Each time
you return to this page, you will get a different puzzle!
___________________________
Answer to Mini-MindBender for Kids
Spaceball
A simple picture or diagram shows that there are 12 planets in Zork's solar
system.
...P1....P2....P3....P4....P5....P6....P7....P8....P9...P10...P11...P12
..Zeek........Zurk..............Zork..............Zook..............Zack
This Mini-MindBender was modified from a puzzle in "The Problem Solver 4" by
Judy Goodnow and Shirley Hoogeboom.
April 1, 1999
MindBender
Two Kids
A boy and a girl are sitting on the front steps.
"I'm a boy," says the kid with black hair.
"I'm a girl," says the kid with red hair.
If at least one of them is lying, what sex are each of the two kids?
___________________________
Mini-MindBender for Kids
DISTRACTION
JUST AN INTERESTING LITTLE DISTRACTION...
It only takes a few seconds. Work this out as you read.
1. First of all, pick the number of days a week that you would
like to eat dinner out.
2. Multiply this number by 2.
3. Add 5.
4. Multiply by 50.
5. If you have already had your birthday this year, add 1749.
If you haven't, add 1748.
6. Last step: Subtract the four digit year that you were born.
You should now have a three digit number (if you are less than 100 years
old):
The first digit of this is your original number (i.e., how many
times you want to eat dinner out each week). The last two digits
are your age!!!
This is the only year (1999) it will ever work, so spread the fun around
while it lasts...
Why does this work?
Can it be modified to work next year?
___________________________
...Answer to MindBender
Two Kids
The four possible true-false combinations for the two statements are TT, TF,
FT, and FF. The first is eliminated because at least one statement is false.
The second and third are eliminated because they result in two boys or two
girls, not one of each. Therefore, both lied. The boy has red hair. The girl
has black hair.
This MindBender was modified from a puzzle in Martin Gardner's book,
"Wheels, Life and Other Mathematical Amusements."
___________________________
Answer to Mini-MindBender for Kids
DISTRACTION
Simple arithmetic shows that:
1) the first number is multiplied by 100 by the combined calculations.
2) the combined calculations result in adding 1998 or 1999 (the year of your
last birthday).
3) Subtracting your year of birth results in your age plus your
original number times 100.
Adding 1 more in step 5 will make it work next year.
5. If you have already had your birthday this year, add 1750.
If you haven't, add 1749.
April 7, 1999
MindBender
Difficult Questions
Marilyn Vos Savant, who writes a weekly column in "Parade" is said to have
the world's highest IQ. People send her some of the toughest questions you
can imagine, almost all of which she is able to answer.
Recently she ran a column of questions she's been sent that she can't
answer.
1. Is there an implied time limit on fortune cookie predictions? If so, how
long is it?
2. Nature shows on television say that when two bull moose compete for a lady
moose, the one with the smaller antlers concedes to the other one. I can see
how a moose can tell the size of his opponent's antlers, but how does he know
how big his own are?
3. Why is it that my lipstick (any brand) doesn't last on my lips for
more than 10 minutes, but it remains on my glass even after it has been
through the dishwasher?
4. When a bank is sold, who gets all that money?
5. In all my years of watching cartoons, I have split brain cells trying to
figure out this puzzling question: How can Donald Duck be an Uncle to Huey,
Dewey and Louie, and they be nephews to his uncles, Scrooge McDuck and Ludwig
Von Drake?
6. I find it curious that there are many individuals whose surname is Brown,
Green, White, Black, Gray or Gold, but there are virtually none whose surname
is Red, Yellow, Orange, Purple or Pink. Is there a logical reason for
this?
7. I am 37 and have been washing my own clothes since I was 10. When I throw
my underpants into the machine, they come out inside out. But if I put them
in inside out, they still come back inside out! Can you explain this?
...There are No Answers to these
perplexing questions.
April 12, 1999
MindBender
XYZ
What three digits are represented by X, Y, and Z in this addition?
XXXX
YYYY
+ ZZZZ
________
YXXXZ
___________________________
Mini-MindBender for Kids
Spare Tire
A man traveled 5,000 miles in a car with one spare tire. He rotated tires at
intervals so that when the trip ended, each tire had been used for the same
number of miles. For how many miles was each tire used?
___________________________
...Answer to MindBender
XYZ
9999
1111
+ 8888
________
19998
From the units column, X+Y=10.
Therefore X+Y+Z is less than 20 and the carry into the tens column is 1.
Therefore, from the tens column, Y+Z=9 and Z is less than 9.
Therefore,
Z=X-1.
Therefore X+Y+Z is less than 19 and the carry into the tens column is 1.
Therefore, X+Y+Z+the carry into the tens column is less than
20.
Therefore, all carrys are 1.
Therefore Y (the carry from the thousands column) is 1.
Therefore X is 9 and Z is 8.
This MindBender was modified from a puzzle in Matthew J. Costello's book,
"The Greatest Puzzles of All Time."
___________________________
Answer to Mini-MindBender for Kids
Spare Tire
Each tire is used 4/5 of the total time. Therefore, each tire has been used
for 4/5 of 5,000 miles, or 4,000 miles.
Another way to look at the problem is:
Total tire-miles traveled is 20,000 or 4 tires times 5,000 miles each.
Each of the 5 tires shares equally in these tire-miles. So each tire
traveled 20,000 divided by 5 or 4,000 miles.
This Mini-MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Circus."
April 19, 1999
MindBender
3 Women
Miss Green, Miss Black, and Miss Blue are out for a stroll together.
One is wearing a green dress, one a black dress, and one a blue dress.
"Isn't it odd," says Miss Blue, "that our dresses match our last
names, but not one of us is wearing a dress that matches her own name?"
"So what," said the woman in black.
What is the color of each woman's dress?
___________________________
Mini-MindBender for Kids
800 Women
In a certain village, there live 800 women. Three percent of them are wearing
one earring. Of the other 97 percent, half are wearing two earrings, half are
wearing none. How many earrings all together are being worn by the women?
___________________________
...Answer to MindBender
3 Women
Miss Blue's dress cannot match her name, so it must be green or black. Since
the woman in black replies to Miss Blue's remark, Miss Blue's dress cannot be
black; therefore Miss Blue is wearing green.
Now consider Miss Black. Her dress cannot be black (or it would match her
name), so it must be green or blue. From above, Miss Blue's dress is green.
Therefore, Miss Black is wearing blue.
By elimination, Miss Green is wearing black.
This MindBender was modified from a puzzle in Matthew J. Costello's book,
"The Greatest Puzzles of All Time."
___________________________
Answer to Mini-MindBender for Kids
800 Women
Among the 97 percent of the women, if half wear two earrings and half none,
this is the same if each wore one. Assuming, then, that each of the 800 women
is wearing one earring, there are 800 earrings in all.
The brute force solution is:
.03*800*1 + .97*.5*800*2 + .97*.5*800*0 = 24 + 776 + 0 = 800
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Magic Show."
April 27, 1999
MindBender
Three Boxes
Three nickels (5 cent coins) and three dimes (10 cent coins) are
distributed in three boxes so that each box holds two coins. The box tops are
marked "Total content is 10 cents," "Total content is 15 cents," and "Total
content is 20 cents." However, someone has switched the box tops so that no
box is labeled correctly. You may not open any box but you are allowed to
shake a box until one coin slides out of a slot at the bottom. What is the
minimum number of coins you must obtain in this way until you know for
certain the contents of all three boxes.
___________________________
Mini-MindBender for Kids
Two Races
Saul and Sal race each other for 100 yards. Sal wins by 10 yards. They decide
to race again, but this time, to even things up, Sal begins ten yards behind
the starting line. Assuming that both run with the same constant speed as
before, who wins this second race?
___________________________
...Answer to MindBender
Three
Boxes
You need only shake one coin from the box incorrectly labeled "Total content
is 15 cents."
If that coin is a dime, the other coin still in that box cannot be a
nickel, because the box would then be correctly labeled. Therefore, the other
coin still in the box is also a dime. The box labeled "Total content is 10
cents" cannot contain two nickels (or it would be correctly labeled), nor can
it contain two dimes, because two of the three dimes available are in the box
labeled "Total content is 15 cents." Therefore, it must contain a dime and a
nickel. This leaves two nickels for the box labeled "Total content is 20
cents."
If the coin removed from the box incorrectly labeled "Total content is 15
cents" is a nickel, the other coin still in that box cannot be a dime,
because the box would then be correctly labeled. Therefore, the other coin
still in the box is also a nickel. The box labeled "Total content is 20
cents" cannot contain two dimes (or it would be correctly labeled), nor can
it contain two nickels, because two of the three nickels available are in the
box labeled "Total content is 15 cents." Therefore, it must contain a dime
and a nickel. This leaves two dimes for the box labeled "Total content is 10
cents."
This MindBender was modified from a puzzle in the Martin Gardner section of
Matthew J. Costello's book, "The Greatest Puzzles of All Time."
___________________________
Answer to Mini-MindBender for Kids
Two Races
Sal wins again. In the first race, she ran 100 yards in the time it
took Saul to run 90 yards. Therefore, in the second race, after Saul has gone
90 yards, Sal will have gone 100 yards, so she will be right alongside him.
Both will have ten yards to go. Since Sal is the faster runner, she will
finish before Saul.
This MindBender was modified from a puzzle in the Martin Gardner section of
Matthew J. Costello's book, "The Greatest Puzzles of All
Time."
May 5, 1999
MindBender
Age Squared
My grandfather, may he rest in peace, told me in 1976, that he was N years
old on his birthday in the year N squared. When was my grandfather born?
___________________________
Mini-MindBender for Kids
Toys
Kimiko's mother and father own a toy store. Today Kimiko and her mother are
buying some tiny clay animals for the store. Her mother likes the seals that
are 22 cents each. Kimiko likes the bears that are 29 cents each. Her mother
gets some of both and pays a total of $5.39. How many of each kind of animal
did Kimiko's mother buy?
___________________________
...Answer to MindBender
Age
Squared
The square root of 1976 is just over 44.
43*43 = 1849, and 1849 is too far before 1976 to be considered.
(Grandfather would have been 127 years old in 1976.)
45*45 = 2025, and 2025 is beyond 1976.
44*44 = 1936. Therefore, my grandfather was 44 on his birthday in 1936.
It follows that he was born in 1892 (1936 - 44).
This MindBender was modified from a puzzle in Martin Gardner's book, "Wheels,
Life and Other Mathematical Amusements."
___________________________
Answer to Mini-MindBender for Kids
Toys
The following chart shows what funds are available for seals if N
bears are purchased at 29 cents each.
N Cost For N Bears Money Left For Seals
---- ---------------- --------------------
1 $0.29 $5.10
2 $0.58 $4.81
3 $0.87 $4.52
4 $1.16 $4.23
5 $1.45 $3.94
6 $1.74 $3.65
7 $2.03 $3.36
8 $2.32 $3.07
9 $2.61 $2.78
10 $2.90 $2.49
11 $3.19 $2.20
12 $3.48 $1.91
13 $3.77 $1.62
14 $4.06 $1.33
15 $4.35 $1.04
16 $4.64 $0.75
17 $4.93 $0.46
18 $5.22 $0.17
The only multiple of 22 cents in the right hand column is $2.20.
Therefore, Kimiko's mother bought 11 bears and 10 seals.
This Mini-MindBender was modified from a puzzle in "The Problem Solver 4" by
Judy Goodnow and Shirley Hoogeboom.
May 5, 1999
Aaron's Birthday
This week's MindBender reminded Solver Aaron Goldman of a riddle of his
regarding his birthday. He has given me permission to share it with the
MindBender list as a bonus MindBender.
Aaron's birthday month and day are squared numbers which when added together
result in another square. The first digit of the two digit year is twice the
square root of the month and the last digit of the two digit year is twice
the square root of the day.
When was he born?
On a side note, if you add the six individual digits in his date of
birth (mo/da/ye m+o+d+a+y+e), you will get his age now. This is not a hint
and is not needed to determine Aaron's birthday. It is just another
interesting mathematical fact about Aaron's birthday.
___________________________
...Answer to Bonus
MindBender
Aaron's Birthday
The only possible squared numbers for the month are 1, 4, and 9.
The only possible squared numbers for the day are 1, 4, 9, 16, and 25.
The only squared number resulting from adding one of the above month numbers
to one of the above day numbers is 9 + 16 = 25.
Therefore, the month is 9 and the day is 16.
The first digit of the two digit year is 2*sqrt(9) = 2*3 = 6.
The second digit of the two digit year is 2*sqrt(16) = 2*4 = 8.
Therefore, Aaron was born on 09/16/68, making him 30 years old.
The individual digits of his date of birth do add up to his current
age (0+9+1+6+6+8 = 30).
Let's remember to wish him a happy 31st birthday on September 16,
1999.
This Bonus MindBender came from MindBender Solver Aaron Goldman. Thanks
Aaron!
May 10, 1999
MindBender
Ice Cream
Three friends (Alex, Bobby, and Chris) eat lunch together every day.
Consider the following true statements:
A. If Alex orders ice cream for dessert, so does Bobby.
B. Either Bobby or Chris always orders ice cream, but never both at the same
lunch.
C. Either Alex or Chris or both always order ice cream.
D. If Chris orders ice cream, so does Alex.
Who orders ice cream and who doesn't?
___________________________
Mini-MindBender for Kids
Money
If nine thousand nine hundred and nine dollars is properly written as $9909,
how should twelve thousand twelve hundred and twelve dollars be written?
___________________________
...Answer to MindBender
Ice Cream
The following chart represents the eight possible combinations with Y
indicating "Yes, they ordered ice cream" and N indicating "No, they did not
order ice cream":
Alex Bobby Chris
1. Y Y Y
2. Y Y N
3. Y N Y
4. Y N N
5. N Y Y
6. N Y N
7. N N Y
8. N N N
Statement A eliminates combinations 3 and 4.
Statement B eliminates combinations 1, 4, 5, and 8.
Statement C eliminates combinations 6 and 8.
Statement D eliminates combinations 5 and 7.
Therefore combination 2 is the only one left. So Alex and Bobby always order
ice cream; Chris never does.
This puzzle is also solvable using Venn diagrams.
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Circus."
___________________________
Answer to Mini-MindBender for Kids
Money
$13212
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Magic Show."
May 17, 1999
MindBender
Missing Number
What is the missing number in the following sequence:
10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, ?, 10000
For two hints, highlight the first two arrows. (but first try to solve without any hint).
Hint Number 1: ...This puzzle is very similar to an earlier
MindBender.
Hint Number 2: ...The missing number is in ternary or base three
notation.
___________________________
Mini-MindBender for Kids
Palindrome
The driver of a car glanced at the odometer and saw that it read 15951 miles.
He said to himself, "That's interesting. The mileage is a palindrome: it
reads the same backward as it reads forward. It will be a long time before
that happens again."
Just exactly two hours later, however, the mileage shown on the
odometer was a new palindrome (the next one possible). What was the car's
average speed for those two hours?
___________________________
...Answer to MindBender
Missing Number
Each number is sixteen in a number system with a different base, starting
with base sixteen and continuing with bases in descending order, ending with
base two. The missing number, sixteen in the ternary or base three system, is
121.
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Magic Show."
___________________________
Answer to Mini-MindBender for Kids
Palindrome
The new palindrome was 16061. The car had traveled 110 miles. The average
speed was 55 miles per hour for those two hours.
This MindBender was modified from a puzzle in Harold R. Jacob's book,
"Mathematics - A Human Endeavor."
May 24, 1999
MindBender
Tri-Hex
An equilateral triangle and a regular hexagon have perimeters of the
same length. If the triangle has an area of two square units, what is
the area of the hexagon?
___________________________
Mini-MindBender for Kids
Coffee
A customer in a restaurant found a dead fly in her coffee. She sent it back
with the waiter for a fresh cup. After taking one sip, she shouted, "This is
the same cup of coffee I had before." How did she know?
___________________________
...Answer to MindBender
Tri-Hex
Three square units.
The hexagon side is one half the side of the equilateral triangle.
The hexagon can be divided into six equilateral triangles that have
sides that are one half the sides of the original equilateral triangle.
The height of these six equilateral triangles making up the hexagon is
one half of the height of the original equilateral triangle.
Therefore, each of these six equilateral triangles making up the
hexagon has an area one fourth of the area of the original equilateral
triangle. Therefore, 6 times .25 times 2 (The square units in the original
equilateral triangle) equals 3.
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Magic Show."
___________________________
Answer to Mini-MindBender for Kids
Coffee
The customer had sugared her original cup of coffee before she found
the dead fly.
This MindBender was modified from a puzzle in Martin Gardner's book,
"Mathematical Magic Show."
May 31, 1999
MindBender
3 Switches
This MindBender came from the Riddle A Day list. I had never seen
it before, and was impressed by its simplicity and elegance.
In a cellar there are three light switches in the OFF position. Each
switch controls 1 of 3 light bulbs on the floor above. You cannot see
the bulbs from the cellar. You may move any of the switches, but you
may only go upstairs one time to inspect the bulbs. How can you
determine which switch controls which bulb with only one trip
upstairs?
___________________________
Mini-MindBender for Kids
Club Members
Terry's club is having a meeting. They have decided that everyone in
the club should have a three digit secret number. They will use just
the numerals 1, 3, and 5 in any secret number, and each club member's
secret number will be different (unique). Each numeral can be used
only once in any secret number. They use all the different three digit
numbers that you can make with the numerals 1, 3, and 5 for the club
members. How many members does Terry's club have?
___________________________
...Answer to MindBender
3 Switches
Turn switch 1 on for five or ten minutes, and then turn it off.
Turn switch 2 on and go check out the bulbs.
The unlit and hot bulb is controlled by switch 1.
The lit bulb is controlled by switch 2.
The unlit and cold bulb is controlled by switch 3.
This MindBender was modified from a puzzle from the Riddle A Day list.
___________________________
Answer to Mini-MindBender for Kids
Club Members
Six.
The only possible secret numbers are 135, 153, 315, 351, 513, and 531.
You can see this by putting one numeral (1, for example) in the
hundreds position. With 1 in the hundreds position, 135 and 153 are
the only possible choices for the secret number. Similarly, with 3 or
5 in the hundreds position, 315 and 351, or 513 and 531 are the only
possible choices for the secret number. The solution can also be
arrived at by realizing that there are 3 choices for the hundreds
digit. Once that digit is chosen, there are only 2 choices left for the
tens digit. Once both the hundreds and tens digit positions are filled,
there is only 1 choice left for the units digit. Thus, the number of
choices possible is 3 * 2 * 1 or 6. This product of all the whole
numbers from 3 down to 1 is called 3! or "3 Factorial." In general, N!
or "N Factorial" is N * (N-1) * (N-2) * ... * 1.
This MindBender was modified from a puzzle in "The Problem Solver 4"
by Judy Goodnow and Shirley Hoogeboom.
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If you have any riddles or MindBenders to add please
e-mail me or
e-mail Mike Avery
PaintSaint helped make this page. check out his
Riddles page.
