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.
July 17, 2000
MindBender
Some Sum Two
Replace letters with digits to make the following sum correct:
.. ABBBC
. + DDDD
. + DDDD
. + DDDD
. + DDDD
_________
.. DDDDD
Try to find all solutions that don't have leading zeros in the numbers
and where all letters are replaced by unique digits (no duplicates).
___________________________
Mini-MindBender for Kids
What's Next
Try this on your friends or family. Tell them you will read them some
numbers. After each number your friend is to immediately say the next
higher number. For example, if you say one hundred fifty-seven, they
should immediately say one hundred fifty-eight, Use the following
numbers:
seventy-two
one hundred twenty-eight
thirteen
five
eight hundred fifty-six
two thousand seven hundred sixty-five
seven hundred eighty-one
thirty-four
five hundred seventy-three
four thousand ninety-nine.
What happened?
___________________________
...Answer to MindBender
Some Sum Two
D is the key to this problem. Trying 1 through 9 for D and determining
C, B, and A (in that order) from the value for D gives us solutions
for all values of D except 1 and 5. The following is one total
solution and value sets for the others, including value sets for the
two failed cases:
.. 13334
. + 2222
. + 2222
. + 2222
. + 2222
_________
.. 22222
(A,B,C,D) = (0,6,7,1) Fails with leading zero.
(A,B,C,D) = (1,3,4,2) The above solution.
(A,B,C,D) = (2,0,1,3)
(A,B,C,D) = (2,6,8,4)
(A,B,C,D) = (3,3,5,5) Fails with duplicate values.
(A,B,C,D) = (4,0,2,6)
(A,B,C,D) = (4,6,9,7)
(A,B,C,D) = (5,3,6,8)
(A,B,C,D) = (6,0,3,9)
This MindBender was modified from a puzzle in Robert M¸ller's book,
"The Great Book of Math Teasers."
___________________________
Answer to Mini-MindBender for Kids
What's Next
Did your friend answer "five thousand" after the last number? Many
people do. But the correct answer is "four thousand one hundred."
How good were your test subjects?
This MindBender was modified from a puzzle in Raymond Blum's book,
"Mathamusements."
July 24, 2000
MindBender
Start Sequence
Usually we ask for a missing number at the end of a sequence. What
is the missing number at the beginning of this sequence?
? 8 5 9 4 10 3 11
___________________________
Mini-MindBender for Kids
Thunderstorm
You see a flash of lightning from a thunderstorm. Then you hear the
BOOM of the thunder. How far away is the storm?
___________________________
...Answer to MindBender
Start Sequence
The missing number is 6. The sequence alternates adding and
subtracting increasing whole numbers starting with adding 2.
6+2=8. 8-3=5. 5+4=9. And so on.
Or the numbers, when taken in an every-other-one fashion, are
8, 9, 10, 11 and ?, 5, 4, 3. These form two sub-sequences, one set
ascending, one descending.
This MindBender was modified from a puzzle in Robert M¸ller's book,
"The Great Book of Math Teasers."
___________________________
Answer to Mini-MindBender for Kids
Thunderstorm
Count seconds (by saying "one thousand one, one thousand two ..." to
yourself) between when you see the lightning and when you hear the
thunder. Divide that number of seconds by 5 to get miles or divide
by 3 to get kilometers. This works because light travels from the
storm to you almost immediately but the sound of the thunder takes
about 5 seconds a mile or about 3 seconds a kilometer to reach you.
Sound travels at about 1100 feet per second or 330 meters per second.
This MindBender was modified from a puzzle in Raymond Blum's book,
"Mathamusements."
July 31, 2000
MindBender
Phone Extension
Mr. Meek is happy with his newly assigned phone extension because it
has four digits, the middle two of which are identical, just like his
name. The repeated center digit is also the first digit of Mr.
Humble's new four digit number. Moreover, Meek's first digit is the
same as the first digit of Mr. Lowly's new four digit number. If you
interchange the first and last digits of Humble's number, you get
Lowly's. If you subtract Lowly's number from Humble's number, you get
Meek's number. So, what is Meek's new phone extension?
___________________________
Mini-MindBender for Kids
4 Letter Word
What four letter word can be placed in front of each of the following
four words to make each of them into a new word?
LINE BOAT LIKE STYLE
___________________________
...Answer to MindBender
Phone Extension
Let Meek's number be ABBC. Then Humble's number can be BDEA and
Lowly's number can be ADEB. The following is the stated subtraction:
.. BDEA
. -ADEB
_______
.. ABBC
B must be greater than A because of the thousands column subtraction.
Therefore, the units subtraction generates a borrow from the tens
column. This means that B must be 9 since the tens column subtraction
is (E-1-E) where the 1 is the units column borrow. Reduce (E-1-E) to
(-1) which isn't allowed, so borrow 10 from the hundreds column which
results in B=9. Since a borrow occurs in the tens column, one also
occurs in the hundreds column for the same reason. Therefore, A is 4
because the thousands column subtraction is (9-1-A=A) where the 1 is
the hundreds column borrow. (9-1-A=A) reduces to (8=2A) or (4=A).
Therefore, C is 5 from the units column subtraction of (4-9). D and E
cannot be uniquely determined, but we were not requested to determine
them. Mr. Meek's new phone extension is 4995.
This MindBender was modified from a problem in the Summer 2000 issue
of "The Bent of Tau Beta Pi" that was lent to me by a friend.
___________________________
Answer to Mini-MindBender for Kids
4 Letter Word
LIFE resulting in:
LIFELINE LIFEBOAT LIFELIKE LIFESTYLE
This MindBender was modified from a puzzle in Victor Serebriakoff's
book, "The Mammoth Book of Astounding Puzzles."
August 7, 2000
MindBender
Change
You have 100 coins which are a mixture of pennies (1 cent), nickels
(5 cents), dimes (10 cents), and quarters (25 cents). You have at
least four of each. The total value of your coins is $2.73. How many
of each coin do you have?
___________________________
Mini-MindBender for Kids
Squares
How many squares of any size are there in the figure below?
-----------------
| . | . | . | . |
-----------------
| . | . | . | . |
-----------------
| . | . | . | . |
-----------------
| . | . | . | . |
-----------------
___________________________
...Answer to MindBender
Change
Four of each coin together total $1.64 in 16 coins. That leaves $1.09
in 84 extra coins. In those extra you must have a number of penny coins
that ends in 4 or 9 or the total cannot be $1.09. If you have 84 extra
pennies, you don't have $1.09. If you have 79 extra pennies, you need 5
other extra coins adding to 30 cents. This is possible only with 4
extra nickels and 1 extra dime. If you have 74 extra pennies, you need
10 other extra coins adding to 35 cents. This is not possible because
even 10 nickels add to more than 35 cents. All other possibilities for
extra pennies (69, 64, etc.), leave similar impossibilities where the
other required coins add to an amount that is too large. Therefore,
from above, you have 79 extra pennies for a total of 83 pennies, 8
nickels, 5 dimes, and 4 quarters.
This MindBender was modified from a problem in the Summer 2000 issue
of "The Bent of Tau Beta Pi" that was lent to me by a friend.
___________________________
Answer to Mini-MindBender for Kids
Squares
30 Squares.
16 squares that are 1X1, 9 squares that are 2X2, 4 squares that are
3X3 and 1 square that is 4X4 for a total of 30 squares. This is the
sum of the first 4 perfect squares starting with 1 squared through 4
squared.
-----------------
| M | N | O | P |
-----------------
| I | J | K | L |
-----------------
| E | F | G | H |
-----------------
| A | B | C | D |
-----------------
The squares start at the lower left corner of the following
identified 1X1 squares:
1X1 squares: A through P (16 squares)
2x2 squares: A through C and E through H and I through K (9 squares)
3X3 squares: A, B, E, and F (4 squares)
4X4 squares: A (1 square).
This MindBender was modified from a puzzle in Victor Serebriakoff's
book, "The Mammoth Book of Mindbending Puzzles."
August 14, 2000
MindBender
Bal/Da
You meet a person from an island where everyone is a truth-teller or
a liar. He doesn't speak English but understands it. You know that
"bal" and "da" mean "yes" and "no" in his language, but you don't
know which is which. You ask him, "Does 'bal' mean 'yes'?" He
responds, "Bal." Do you now know which ("bal" or "da") means "yes"?
Is the person a truth-teller or liar?
___________________________
Mini-MindBender for Kids
Birthdays
How many people do you think need to be in a room before there is
at least a fifty-fifty chance that at least two of them will have
the same birthday?
___________________________
...Answer to MindBender
Bal/Da
If "bal" means "yes," then only a truth-teller would answer "bal,"
the truthful answer. If "bal" means "no," then only a truth-teller
would answer "bal," the truthful answer. Therefore, the person is a
truth-teller, but you still don't know which ("bal" or "da") means
"yes."
This MindBender was modified from a puzzle in Raymond Smullyan's book,
"What Is the Name of This Book."
___________________________
Answer to Mini-MindBender for Kids
Birthdays
Only 23. Seems amazing doesn't it? Try it the first day of school
in your classroom.
This MindBender was modified from a puzzle in Adam Hart-Davis' book,
"Amazing Math Puzzles."
August 21, 2000
MindBender
Another Lie
I met two people, A and B, from an island where everyone is a
truth-teller or a liar. A said that B is a liar. B said that A is a
truth-teller. What can you conclude from this?
___________________________
Mini-MindBender for Kids
Symmetric Addition
Here's an interesting thing about perfect squares (an integer times
itself). Look at the following equations. Do you notice anything
unusual?
1 = 1 = 1*1
1+2+1 = 4 = 2*2
1+2+3+2+1 =9 = 3*3
1+2+3+4+3+2+1 =16 = 4*4
___________________________
...Answer to MindBender
Another Lie
You can conclude that "I" am a liar. I couldn't have been told both
these things. A must either be a truth-teller or a liar. Case 1.)
Assume A is a truth-teller. Then B is a liar (from A's statement). But
then, B's statement is false, so A is a liar. This is a contradiction
from Case 1's assumption that A is a truth-teller. Case 2.) Assume A
is a liar. Then B is a truth-teller (from A's statement). But then,
B's statement is true, so A is a truth-teller. This is a
contradiction from Case 2's assumption that A is a liar.
This MindBender was modified from a puzzle in Raymond Smullyan's book,
"What Is the Name of This Book."
___________________________
Answer to Mini-MindBender for Kids
Symmetric Addition
If you add all the integers from 1 up to N together and then continue
to add to that sum all the integers from (N-1) down to 1, you end up
with N*N or N squared. This works for all positive integers.
The reason that N*N is called "N squared" is because it is in effect
the area of a square of side N. This can be represented as N rows of
N balls each, in a grid. Now suppose you split this grid of balls into
two triangles, along the side of the diagonal. One of these is a right
triangle with the base of N balls, while the other is a right triangle
with a base of N-1 balls. The number of balls in the first triangle is
1+2+...+N where N is the base, and the number for the second is
1+2+...+N-1. Add these two totals together and we get the equations
above. Leading periods are used to maintain spacing. An example with N=7:
The 7X7 square with asterisks as the balls
*******
*******
*******
*******
*******
*******
*******
Splits into:
******* This is the right triangle base of 7 or N balls.
******
*****
****
***
**
*
and
..... *
.... **
... ***
.. ****
. *****
.****** This is the right triangle base of 6 or N-1 balls.
This MindBender was modified from a puzzle in Adam Hart-Davis' book,
"Amazing Math Puzzles."
August 28, 2000
MindBender
100 Men
In a town there are 100 men. 85 are married. 70 have a cell phone.
75 own a car. 80 own their own home. What is the least possible
number who are married, have a cell phone, own a car, and own their
own home?
___________________________
Mini-MindBender for Kids
Eggs
You have three boxes of eggs containing 21, 9, and 6 eggs. You want
to use TWO moves to end up with 3 boxes, each with 12 eggs. How can
you do this if each move consists of doubling the number of eggs in
one box by taking the required eggs from ONE other box?
___________________________
...Answer to MindBender
100 Men
Look at how many do "not" satisfy each individual requirement. 15
are not married. 30 do not have a cell phone. 25 do not have a car.
20 do not own their own home. It is possible that these 90 men
(15+30+25+20) are all different men. This would leave only 10 men
with wife, cell phone, car, and house.
This MindBender was modified from a puzzle in Pierre Berloquin's book,
"100 Numerical Games."
___________________________
Answer to Mini-MindBender for Kids
Eggs
The starting point is with the baskets holding 21,9,6. Then move so
the baskets hold 12,18,6. Then move so the baskets hold 12,12,12.
This MindBender was modified from a puzzle in David J. Bodycombe's
book, "The Mammoth Puzzle Carnival."
September 5, 2000
MindBender
Running Dog
A dog is walking with one of its owners, Jeff, when he spots his
other owner, Suzie, 300 feet away. The dog runs off to meet Suzie. As
soon as the dog gets to Suzie, he turns around and runs back to Jeff.
The dog continues to run back and forth between its owners. Jeff and
Suzie are walking towards each other the whole time. Jeff walks at 3
feet per second. Suzie walks at 2 feet per second. The dog runs at 6
feet per second. Assuming it takes no time for the dog to turn
around, what total distance has the dog run when Jeff and Suzie
eventually meet?
___________________________
Mini-MindBender for Kids
More Eggs
A MindBender similar to last week's but this week we want a solution,
but not the best solution as we asked for last week.
You have three boxes of eggs containing 21, 9, and 6 eggs. You want
to use THREE moves to end up with 3 boxes, each with 12 eggs. How can
you do this if each move consists of doubling the number of eggs in
one box by taking the required eggs from ONE other box?
___________________________
...Answer to MindBender
Running Dog
Relative to each other, Jeff and Suzie are travelling at 5 feet per
second (3+2). Therefore, it will take 300/5 or 60 seconds for them to
meet. In those 60 seconds, the dog will have run 60*6 or 360 feet.
This MindBender was modified from a puzzle in David J. Bodycombe's
book, "The Mammoth Puzzle Carnival."
___________________________
Answer to Mini-MindBender for Kids
More Eggs
One possible solution:
The starting point is with the baskets holding 21,9,6. Then move so
the baskets hold 15,9,12. Then move so the baskets hold 6,18,12.
Then move so the baskets hold 12,12,12. Other solutions are also
possible.
This MindBender was modified from a puzzle in David J. Bodycombe's
book, "The Mammoth Puzzle Carnival."
September 11, 2000
MindBender
Cryptogram
Today's MindBender is a Cryptogram, or as some call them, a Cryptoquip.
Each letter stands for another. If you think Q=P, for example, Q
would equal P throughout the puzzle. Decode the following:
Cryptogram Clue: Q equals P
FGKJ QMGHJS LH EGBMPOE GV KPEV LBOVASGH QGOVBJE: QBR VAJ VGBM PR VAJ SBRFAH.
Second Cryptogram Clue if desired:
J equals E
___________________________
Mini-MindBender for Kids
Subtraction
I saw the following equation and comment written on a mathematics
classroom blackboard:
120
-22
---
=21 This is absolutely correct!
How can this be so?
___________________________
...Answer to MindBender
Cryptogram
GAME PLAYED BY SAILORS AT MOST BIRTHDAY PARTIES: PIN THE TAIL ON THE DINGHY.
This Cryptogram came from the Minneapolis Star Tribune newspaper.
___________________________
Answer to Mini-MindBender for Kids
Subtraction
The numbers are in the Base 3 number system, where 2 is the largest
digit that can be used. Each successive position to the left (from
the right end position in a number) has its value multiplied by the
next higher power of three. This is just as it works in our usual
Base 10 number system except that those numbers use powers of 10.
For example, 673 (in Base 10) equals
3*(10**0) + 7*(10**1) + 6*(10**2) = 3*1 + 7*10 + 6*100 = 3+70+600
Therefore, the equation in Base 3 can be converted to Base 10:
120 = 0*(3**0) + 2*(3**1) + 1*(3**2) = 0*1 + 2*3 + 1*9 = 0+6+9 = 15
-22 = 2*(3**0) + 2*(3**1) = 2*1 + 2*3 = 2+6 = 8
---
=21 = 1*(3**0) + 2*(3**1) = 1*1 + 2*3 = 1+6 = 7
and 15 - 8 does equal 7.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
September 18, 2000
MindBender
Quarters
You and another player are introduced to a game involving quarters
(coins). Each of you has an adequate supply of quarters. The game
is played by each of you taking turns placing a single quarter flat
onto a circular table. The last person who CANNOT fit a quarter
onto the table loses. Quarters cannot be stacked. The size of the
table is unknown. In order to ALWAYS win, would you go first or
second? What would be your strategy and why?
___________________________
Mini-MindBender for Kids
Four Across
Six coins are arranged in the shape of a cross with four coins down
and three coins across. Move only one coin so that there are four
coins in each direction. Leading periods are used to maintain spacing.
. O
.OOO
. O
. O
How can this be so?
___________________________
...Answer to MindBender
Quarters
The following is my strategy:
Choose to go first and put your first quarter in the absolute or dead
center of the table. If there is not room for another quarter (a very
small table), you win. After your opponent makes his move, place your
quarter in the mirror position relative to the first ( or center)
quarter placed. This way, if your opponent could make a move, you can
always make a move. Eventually your opponent won't be able to move
and you win. This strategy works for round, square, rectangular,
hexagonal, octagonal, etc. tables, not just round ones, since all
those tables are symmetric with respect to the center point.
This MindBender was modified from a puzzle submitted by Stephen Tsai,
one of our MindBender Solvers.
___________________________
Answer to Mini-MindBender for Kids
Four Across
Move the bottom coin, Y, and place it on top of the coin at position X.
Leading periods are used to maintain spacing.
. O
.OXO
. O
. Y
This MindBender was modified from a puzzle in Raymond Blum's book,
"Math Trick, Puzzles & Games."
September 25, 2000
MindBender
Plus/Minus
Leading periods are used to maintain spacing.
Solve the following dual cryptarithmetic:
.. XYZ ... XYZ
.. +AB ... -AB
.. ___ ... ___
. CDEF ... BGA
Both the addition and the subtraction use the same substitution.
___________________________
Mini-MindBender for Kids
Coins
Leading periods are used to maintain spacing.
Ten coins are arranged in a triangle like:
.... O
... O O
.. O O O
. O O O O
Move only 3 coins to change them to be like:
. O O O O
.. O O O
... O O
.... O
___________________________
...Answer to MindBender
Plus/Minus
Leading periods are used to maintain spacing.
C must be 1. X must be 9. D must be 0. Therefore, B must be 8. That
leaves only 2, 3, 4, 5, 6, and 7. Z cannot be 2 or 3 because of the
units column addition. Z cannot be 6 or 7 because of the units
column subtraction. Trying Z as 4 and 5 gives us the only possible
answer:
.. 945 ... 945
.. +78 ... -78
.. ___ ... ___
. 1023 ... 867
This MindBender was modified from a puzzle in Pierre Berloquin's book,
"100 Numerical Games."
___________________________
Answer to Mini-MindBender for Kids
Coins
Leading periods are used to maintain spacing.
Move coins X, Y, and Z
.... X
... A B
.. C D E
. Y F G Z
to the following spots:
. X A B Y
.. C D E
... F G
.... Z
My youngest daughter, Katie, gave me this MindBender.
Thanks, Katie!
October 2, 2000
MindBender
Spouse-To-Be
Joe works with five women: Ada, Betty, Carol, Deb, and Eve.
1. The women are in two age brackets: three women are under thirty
and two are over thirty.
2. Two women are teachers. The other three women are doctors.
3. Ada and Carol are in the same age bracket.
4. Deb and Eve are in different age brackets.
5. Betty and Eve have the same occupation.
6. Carol and Deb have different occupations.
7. Of the five women, Joe will marry the teacher over thirty.
Whom will Joe marry?
___________________________
Mini-MindBender for Kids
Average Grade
Chris' grades in three courses are 87, 92, and 79 respectively. The
credit hours for these three courses are 6, 8, and 2 respectively.
What would Chris' overall grade average be for the three courses
combined?
___________________________
...Answer to MindBender
Spouse-To-Be
From 1, 3, and 4, either Deb or Eve must be in the same age bracket
as Ada and Carol. Therefore, Ada and Carol are under 30. From 7, Joe
will not marry Ada or Carol.
From 2, 5, and 6, either Carol or Deb must have the same occupation
as Betty and Eve. Therefore, Betty and Eve are doctors. From 7, Joe
will not marry Betty or Eve.
By elimination, Joe will marry Deb.
Although not requested, the complete characteristics of the five women
are:
Ada, Carol, and Eve are under thirty. Betty and Deb are over thirty.
Ada and Deb are teachers. Betty, Carol, and Eve are doctors.
This MindBender was modified from a puzzle in George J. Summers' book,
"Test Your Logic."
___________________________
Answer to Mini-MindBender for Kids
Average Grade
88.5. Each course grade must be "weighted" by its credit hours.
(6*87 + 8*92 + 2*79)/(6+8+2) = 88.5.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
October 9, 2000
MindBender
What Base
What number base is required to make 321 equal 41 decimal?
___________________________
Mini-MindBender for Kids
Bus
You're driving a bus that is leaving from Pennsylvania and your
destination is New York.
To start off with, there are 32 passengers on the bus.
At the first bus stop, 11 people get off and 9 people get on the bus.
At the next bus stop, 2 people get on and 2 people get off the bus.
At the next bus stop, 16 people get off and 12 people get on the bus.
At the next bus stop, 5 people get on and 3 people get off the bus.
Now, what color are the bus driver's eyes?
___________________________
...Answer to MindBender
What Base
This question can be answered by solving the following equation:
3*X*X + 2*X + 1 = 41
This quadratic equation has two solutions, 10/3 and -4.
-4 is the answer I was looking for, since any number can be represented
as a number in base N, OR in base -N, where N is a non-zero integer.
And that is a very interesting mathematical fact.
The MindBender moderator is the source for this MindBender.
___________________________
Answer to Mini-MindBender for Kids
Bus
The key to understanding the problem is focusing on the right
information. If we assume it is critical to keep track of the number
of people getting on and off the bus, we focus on information that
turns out to be unessential. It distracts us from the important
information.
The answer to the problem is found in the first sentence: YOU are
driving the bus, so the color of the bus driver's eyes is, of course,
the color of YOUR eyes.
Oh, by the way, there are now 28 passengers on the bus.
This Mini-MindBender was modified from a puzzle sent to me by a
MindBender Solver who saw it on a chat list.
Next Page
Other Pages
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.
