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.
October 16, 2000
MindBender
Ages
When Tim is as old as his father is now, Tim's sister will be twice as
old as she is now and the age of his father will be twice the age Tim
will be when his sister is as old as his father is now. The total of
the ages of Tim, his sister, and his father is a century.
How old is everyone?
___________________________
Mini-MindBender for Kids
Spelling
Sometimes even just words can be puzzling. The following words are all
misspelled:
seperate tyrrany grammer exagerate yeild irresistable definately
inadvertant indispensible comendable excede questionaire dissippate
liason athelete existance millenium desireable
Can you provide the correct spelling for each of the above words?
___________________________
...Answer to MindBender
Ages
Let the ages be T, S, F for Tim, Tim's sister, and Tim's father. Then we
have T+S+F=100 from the last statement and T+X=F and S+X=2S from the
first part of the first statement, so X=S and T+S=F, so F=50. From the
second part of the first statement, we have F+X=2(T+Y) or 50+S=2(T+Y)
and S+Y=50. But, S+T=50 so Y=T. So 50+S=2(T+T) or S=4T-50 and S=50-T.
This gives us 4T-50=50-T or 5T=100 or T=20. Therefore, S=30.
Tim is 20. Tim's sister is 30. Tim's father is 50.
This MindBender was modified from a puzzle in Pierre Berloquin's book,
"100 Numerical Games."
___________________________
Answer to Mini-MindBender for Kids
Spelling
The following are the correct spellings:
separate tyranny grammar exaggerate yield irresistible definitely
inadvertent indispensable commendable exceed questionnaire dissipate
liaison athlete existence millennium desirable
This MindBender was modified from an advertisement for Dodge vehicles.
October 23, 2000
MindBender
Four Groups
Can you place the 12 numbers (1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6) into
four groups so that each group shares a number with every other group
and the total sum of each group is even?
___________________________
Mini-MindBender for Kids
Word Transition
Can you change SALT to MINE in exactly four steps, changing one letter
each step and always creating a good English word at each step?
SALT
....
....
....
MINE
___________________________
...Answer to MindBender
Four Groups
A couple example solutions are:
1,2,3 1,4,5 2,4,6 3,5,6
1,3,6 1,5,4 2,3,5 2,4,6
Other solutions are also possible.
My approach to solution one above was as follows:
Put 3 numbers in the first group so its sum is even (1,2,3). Put those
numbers separately in the other groups -- 1 in the second group and 2
in the third group and 3 in the fourth group. Put two unused numbers
(4,5) in the second group so its total is even. Put those two numbers
separately in the remaining two groups -- 4 in the third group and 5
in the fourth group. Put the last unused number (6) in the third and
fourth groups. Ensure that all groups sum to an even number.
This MindBender was modified from a puzzle in David J. Bodycombe's
book, "The Mammoth Puzzle Carnival."
___________________________
Answer to Mini-MindBender for Kids
Word Transition
One Solution is:
SALT
MALT
MALE
MILE
MINE
This MindBender was modified from a puzzle in Victor Serebriakoff's
book, "The Mammoth Book of Astounding Puzzles."
October 30, 2000
MindBender
Tennis
Four people played a game of tennis. The four people were Suzie,
her father Bill, her husband Jeff, and their daughter Abby. After
the game, one of the four players spoke truthfully about one time
during the game. That player said:
1. I was directly across the net from the server's daughter.
2. My partner (on the same side of the net as I) was directly
across the net from the receiver's father.
3. The server was diagonally across the net from the receiver
(of course).
Which player was speaking?
___________________________
Mini-MindBender for Kids
Painting
I did some painting this weekend. The room was 12 feet X 15 feet and
I painted the walls (8 feet tall) and the ceiling. For this
Mini-MindBender, assume the room had no windows and no doors. This
is just an assumption, since if it really had no doors or windows,
how did my wife know it needed to be painted? If I normally use a
gallon of wall paint and a gallon of ceiling paint to paint a room
that is 10 feet by 12 feet, how much paint did I use this weekend?
___________________________
...Answer to MindBender
Tennis
Make a chart of the tennis court showing the facts. It will look
like:
Receiver's father | Server's daughter
Bill or Jeff | Suzie or Abby
Not the Receiver | Not the Server
_______________________________________
_______________________________________
Speaker's Partner | Speaker
Not the Receiver | Not the Server
|
Trying the four cases possible (Bill or Jeff in upper left, and
Suzie or Abby in upper right) leads to only one possibility:
Receiver's father | Server's daughter
Jeff | Abby
| Receiver
_______________________________________
_______________________________________
Speaker's Partner | Speaker
Suzie | Bill
Server |
Which means that Suzie's father, Bill, was the speaker.
This MindBender was modified from a puzzle in George J. Summers' book,
"The Great Book of Mind Teasers & Mind Puzzlers."
___________________________
Answer to Mini-MindBender for Kids
Painting
For the ceiling, (12*15)/(10*12) = 15/10 = 1.5 gallons or a gallon
and a half.
The answer is different for the walls:
((12+15+12+15)*8)/((10+12+10+12)*8) = (54*8)/(44*8) = 54/44 ~= 1.227
gallons or about a gallon and a quart.
The MindBender moderator is the source for this Mini-MindBender.
November 6, 2000
MindBender
House Number
My house has a number.
1) If my house number is a multiple of 3, then it is a number from
50 to 59.
2) If my house number is not a multiple of 4, then it is a number
from 60 to 69.
3) If my house number is not a multiple of 6, then it is a number
from 70 to 79.
What is my house number?
___________________________
Mini-MindBender for Kids
Numbers
How many different four digit numbers can you make by using the
digits 2, 5, 7, and 8 if each four digit number must contain all
four of the digits 2, 5, 7, and 8?
___________________________
...Answer to MindBender
House Number
Consider the numbers:
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
Suppose my house number is a multiple of 3. Then from 1), it is
either 51, 54, or 57. But from 2), it cannot be any of these three
since none is a multiple of 4. Therefore my house number is not a
multiple of 3.
Then my house number is not a multiple of 6 because 6 is a multiple
of 3. So, from 3), it is a number from 70 to 79. Then because it is
not a multiple of 3, it is either 70, 71, 73, 74, 76, 77, or 79.
From 2), it cannot be "not a multiple of 4," so it is a multiple of
4. Therefore, my house number is 76 because that is the only number
of 70, 71, 73, 74, 76, 77, or 79 that is a multiple of 4.
This MindBender was modified from a puzzle in George J. Summers' book,
"The Great Book of Mind Teasers & Mind Puzzlers."
___________________________
Answer to Mini-MindBender for Kids
Numbers
The answer is twenty-four numbers. You can choose from four digits
for the thousands digit, then choose from three remaining digits for
the hundreds digit, then choose from two remaining digits for the
tens digit, then choose the last digit for the ones digit. Another
approach is to enumerate all possible answers:
2578 2587 2758 2785 2857 2875
5278 5287 5728 5782 5827 5872
7258 7285 7528 7582 7825 7852
8257 8275 8527 8572 8725 8752
This MindBender was modified from a puzzle in "The Problem Solver 4"
by Judy Goodnow and Shirley Hoogeboom.
November 13, 2000
MindBender
Sequence
What is the next number in the following sequence?
1 32 81 64 25 6 ?
___________________________
Mini-MindBender for Kids
Sequence
What is the missing number in the following sequence?
1:3, 2:3, 3:5, 4:4, 5:4, 6:3, 7:5, 8:5, 9:4, 10:?
___________________________
...Answer to MindBender
Sequence
The missing number is 1.
The sequence is determined as follows:
1**6 2**5 3**4 4**3 5**2 6**1 7**0 and 7**0 is 1. (Actually anything
to the zero power is 1.)
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
___________________________
Answer to Mini-MindBender for Kids
Sequence
The missing number is 3.
The number of letters it takes to spell the first number of each
pair is the second number of each pair.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
November 20, 2000
MindBender
Triangle
Find the pattern and determine what the next line in the following triangle is?
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
___________________________
Mini-MindBender for Kids
Highways
My wife and I recently went on a little weekend trip. Figure out
the numbers of the highways that we used.
The first highway number was the product of the third and fourth odd
numbers. The second highway number was the first highway number plus
400. The third highway number was the first highway number plus the
second highway number minus the fourth highway number, all divided
by 6. The fourth highway number was the second highway number
divided by 10 and rounded up to a whole number. The fifth highway
number was the sum of the first four highway numbers divided by 9.
___________________________
...Answer to MindBender
Triangle
The next line is:
1 3 1 1 2 2 2 1
and the whole triangle is:
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1
The pattern is to simply read the previous line, producing the next line. For example, the line I
added is a description of line 6: one 3, one 1, two 2s, two 1s OR
1 3 1 1 2 2 2 1
This MindBender was modified from a puzzle submitted by Stephen Tsai,
one of our MindBender Solvers. I have also seen it before.
___________________________
Answer to Mini-MindBender for Kids
Highways
Calculate the highway numbers in the following order:
First Highway Number: 35 (5*7)
Second Highway Number: 435 (35+400)
Fourth Highway Number: 44 (435/10 and rounded up)
Third Highway Number: 71 ((35+435-44)/6)
Fifth Highway Number: 65 ((35+435+71+44)/9)
The MindBender moderator is the source for this Mini-MindBender.
November 27, 2000
MindBender
Poker
In a game of poker, one of the hands of five cards had the following features:
A. There was no card above a 10 (an ace is above a 10 in poker).
B. No two cards were of the same value.
C. All four suits were represented.
D. The total values of the odd and even cards were equal.
E. No three cards were in sequence.
F. The black cards totaled 10 in value.
G. The hearts totaled 14.
H. The lowest card was a spade.
What was the hand?
___________________________
Mini-MindBender for Kids
Fleas
Two dogs, Captain and Champ, each have some fleas. If one flea jumps
from Captain to Champ, they both would have the same number. If one
flea jumps from Champ to Captain, Captain would have five times as
many as Champ. How many fleas does each dog have?
___________________________
...Answer to MindBender
Poker
Two of spades, nine of hearts, five of hearts, four of diamonds and the
8 of clubs.
Starting with B, C, and G results in the hand holding two hearts, either
the 10 and 4, the 8 and 6, or the 9 and 5. If the hearts are 8 and 6,
then from F and H, the spade and club must be 2 and 8 (violates B), 3 and
7 (violates E), 4 and 6 (violates B), or 5 and 5 (violates B). Therefore,
the hearts are not 8 and 6. If the hearts are 10 and 4, then from F,
the spade and club must be 2 and 8 (the diamond would need to be odd and
24), 3 and 7 (the diamond would have to be odd and 4), 4 and 6 (violates
B), or 5 and 5 (violates B). Therefore, the hearts are not 10 and 4. So
the hearts are 9 and 5. Then from F, the spade and club must be 3 and 7
(the diamond would have to be 24), 4 and 6 (violates E), 5 and 5
(violates B), or 2 and 8 with the diamond being a 4. This is the solution.
This MindBender was modified from a puzzle in Tim Sole's and Rod Marshall's
book, "Nearly Impossible Brain Bafflers." This MindBender also appeared on
The Daily Tease. If you would like to subscribe to The Daily Tease, please
visit:
http://www.thedailytease.com
___________________________
Answer to Mini-MindBender for Kids
Fleas
Champ has two fleas and Captain has four.
Using K for the number of Captain's fleas and C for Champ's, we have:
K-1=C+1 or K=C+2
K+1=5(C-1) or C+2+1=5C-5 or 4C=8 or C=2 so K=4
This MindBender was modified from a puzzle in Adam Hart-Davis' book,
"Amazing Math Puzzles."
December 4, 2000
MindBender
Three Ds
In the multiplication problem below, each letter represents a
different digit. What digit does D represent?
A
CB
_____
ED
GF
_____
DDD
___________________________
Mini-MindBender for Kids
What Number
I am thinking of a five digit number.
A. The first digit is the sum of the last two digits.
B. The second digit is twice the first digit and is also three times the fourth digit.
C. The total of all five digits is 16.
What is the number I have in mind?
___________________________
...Answer to MindBender
Three Ds
A * CB = DDD
A * CB = D * 111
A * CB = D * 3 * 37
So CB is 37 or 74
If CB is 37, A = 3 * D
If CB is 74, 2 * A = 3 * D
So there are six possible value sets for CB, D, and A.
CB D A
A) 37 1 3
B) 37 2 6
C) 37 3 9
D) 74 2 3
E) 74 4 6
F) 74 6 9
Since each letter represents a different digit, A), C), and E) are
eliminated. Doing the remaining three multiplications eliminates
D) and F) because E=F and D=G. This leaves case B), where D = 2.
This MindBender was modified from a puzzle in George J. Summers' book,
"Test Your Logic."
___________________________
Answer to Mini-MindBender for Kids
What Number
From B, the second digit is 6 and the first digit is 3 and the
fourth digit is 2. From A and the fact that the fourth digit is two,
the fifth digit is 1. From C and the digits we have already
determined, the third digit is 4.
Therefore, the number is 36421.
This MindBender was modified from a puzzle in Victor Serebriakoff's
book, "The Mammoth Book of Mindbending Puzzles."
December 11, 2000
MindBender
Equations
Use the following set of five equations
1) A+B=Z
2) Z+P=T
3) T+A=F
4) B+P+F=100
5) A=8
to determine the value of F.
___________________________
Mini-MindBender for Kids
Sequence
What is the next number in the following sequence
1 8 11 18 80 81 82 83 84 85 86 87 88 89 100 ?
Hint: Consider each "number" carefully.
___________________________
...Answer to MindBender
Equations
Not all values can be determined since we have 5 equations in six
unknowns. However, we can determine F as follows:
1) and 5) result in B=Z-8
2) results in P=T-Z
3) and 5) result in F=T+8
Substituting the above equalities for B, P, and F into 4) results in
(Z-8)+(T-Z)+(T+8)=100 or 2T=100 or T=50
Using T=50, 3), and 5) results in 50+8=F, so F=58.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
___________________________
Answer to Mini-MindBender for Kids
Sequence
101. These are the whole numbers, starting with "One," that start
with a vowel.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
December 18, 2000
MindBender
A Special Number
Find the smallest four digit number (first digit not zero) that leaves
a remainder of 1 when divided by 3, a remainder of 0 when divided by 5,
a remainder of 0 when divided by 7, and a remainder of 4 when divided
by 11.
___________________________
Mini-MindBender for Kids
Average Speed
A pilot flies in a very fast jet for two hours at a speed of 840
miles per hour to arrive at the destination. The pilot then flies
in a small plane back to the starting point at 120 miles per hour.
What is the pilot's average speed for the total trip?
___________________________
...Answer to MindBender
A Special Number
For the non-zero remainders, determine a multiple of the product of
the other divisors that has the desired remainder. Then add those
numbers together, and if necessary, deduct the product of all the
divisors as many times as necessary to arrive at the desired smallest
four digit number. In this case, 5*7*11=385 already has a remainder
of 1 when divided by 3. 3*5*7=105 has a remainder of 6 when divided
by 11. But 8*105=840 has a remainder of 4 when divided by 11. Add 385
to 840 resulting in 1225. No deduction of 1155 (3*5*7*11) is
necessary, so ...
The answer is 1225, or December 25, or Merry Christmas!
Happy Holidays to all the MindBender Solvers!
The MindBender moderator is the source for this MindBender.
___________________________
Answer to Mini-MindBender for Kids
Average Speed
The pilot flew 1680 miles to arrive at the destination (2 hours
times 840 miles per hour). The pilot flew for 14 hours on the return
flight (1680/120). So his average speed was 210 miles per hour
(1680 + 1680) / (2+14) = 3360/16 = 210.
This MindBender was modified from a puzzle in Victor Serebriakoff's
book, "The Mammoth Book of Astounding Puzzles."
December 26, 2000
MindBender
Another Special Number
Find the smallest four digit number (first digit not zero) that leaves
a remainder of 6 when divided by 35, a remainder of 21 when divided by
36, and a remainder of 3 when divided by 37.
___________________________
Mini-MindBender for Kids
What Are They
Between 1 and 100, there are 25 of them.
Between 100 and 200, there are 21 of them.
Between 200 and 300, there are 16 of them.
Between 400 and 500, there are 17 of them.
What are they?
___________________________
...Answer to MindBender
Another Special Number
For each remainder, determine a multiple of the product of the other
divisors that has the desired remainder. Then add those numbers
together, and if necessary, deduct the product of all the divisors
as many times as necessary to arrive at the desired smallest four
digit number. In this case, 36*37=1332 needs to be multiplied by 3
(3996) to have a remainder of 6 when divided by 35. 35*37=1295
needs to be multiplied by 15 (19425) to have a remainder of 21 when
divided by 36. 35*36=1260 needs to be multiplied by 20 (25200) to
have a remainder of 3 when divided by 37. Add 3996, 19425, and
25200 to get 48621. Deduct 46620 (35*36*37) to arrive at the answer
of 2001.
The answer is 2001, or the New Year, or Happy New Year!
A Happy and Healthy New Year to all the MindBender Solvers!
The MindBender moderator is the source for this MindBender.
___________________________
Answer to Mini-MindBender for Kids
What Are They
Prime numbers, numbers whose only factors are 1 and themselves.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
January 2, 2001
MindBender
Name Worths
James is worth 23. Suzie is worth 22. Jane is worth 18. Using this
system, how much is Rachel worth?
___________________________
Mini-MindBender for Kids
Unique Time
Yesterday, at a very early time of the day, a rare mathematical event
occurred. What was the event and what time did it occur?
___________________________
...Answer to MindBender
Name Worths
28. Add 5 for each consonant and 4 for each vowel.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's
"The Mensa 365 Brain Puzzlers Calendar" for 2001.
___________________________
Answer to Mini-MindBender for Kids
Unique Time
The event was an unusual time, down to the hundredth of a second. It
occurred at one and one-hundredth of a second past one minute after
one AM. The date and time were expressed using only '01':
01/01/01 01:01:01.01.
The MindBender moderator is the source for this Mini-MindBender.
January 8, 2001
MindBender
Married Men
5/6 of all men in a certain location are married. 1/2 of the women in
the same location are married. All spouses are in this location. What
fraction of this whole group are single men?
___________________________
Mini-MindBender for Kids
T-Shirts
Molly sold 6,000 T-shirts last year, which was 140% more than she
sold the year before. How many did she sell the year before?
___________________________
...Answer to MindBender
Married Men
There are many ways to solve this problem. The following is one way:
5/6 of all men are married. This is the same number or amount as the
married women. It is also the same number or amount as the single
women (since an equal numbers of women are married). 1/6 of the men
are single. Let 1/6 of the men be called A. Then the total group is
A+5A+5A+5A or 16A. Then the single men's fraction is A/16A or 1/16.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
___________________________
Answer to Mini-MindBender for Kids
T-Shirts
Let T be the T-shirts sold the year before. Then we have:
6000 = T +1.4*T
6000 = 2.4*T
T = 2500
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
January 15, 2001
MindBender
What If
If 1/3 of 1/5 = 1/7, what does 1/5 of 1/9 equal?
___________________________
Mini-MindBender for Kids
Missing Number
Find the missing number in the following pairs of numbers:
1 0
2 7
3 26
4 63
5 ?
___________________________
...Answer to MindBender
What If
Set up a proportion:
(1/3 * 1/5) / (1/7) = (1/5 * 1/9) / X
Reducing and cross multiplying results in:
1/15 * X = 1/315
So X = 15/315 = 1/21
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
___________________________
Answer to Mini-MindBender for Kids
Missing Number
The missing number is 124. The second number in each pair is one less
than the cube of the first number in the pair.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
January 22, 2001
MindBender
A Series
What is the next number in the following series and why?
1 33554432 43046721 262144 625 ?
___________________________
Mini-MindBender for Kids
Wrong Word
One of the following words does not belong with the others. Which one
and why?
gnome comfort knife wrought blaze subtle aisle pneumonia
___________________________
...Answer to MindBender
A Series
6. The series can be written as:
1**36 2**25 3**16 4**9 5**4 6**1
where the exponents go down successively by 11, 9, 7, 5, and 3.
Or the series can be written as:
1**(6**2) 2**(5**2) 3**(4**2) 4**(3**2) 5**(2**2) 6**(1**1)
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
___________________________
Answer to Mini-MindBender for Kids
Wrong Word
Comfort does not belong. It does not have any silent letters.
This MindBender was modified from a puzzle in Jerry Stickels'
"Mindbending Puzzles" calendar for 2000.
January 29, 2001
MindBender
Henry Ford Quote
Decode the following cryptogram (a quote from Henry Ford):
J SFBMMZ EPO'U UIJOL QFPQMF XJMM FWFS MPWF DBST UIF XBZ UIFZ MPWF
UIFJS IPSTFT.
___________________________
Mini-MindBender for Kids
Four Digits
Solve the following addition. The letters A,B,C,D are 1,2,3,4 but not
necessarily in that order.
DD
+BC
---
CA
___________________________
...Answer to MindBender
Henry Ford Quote
I REALLY DON'T THINK PEOPLE WILL EVER LOVE CARS THE WAY THEY LOVE
THEIR HORSES.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's
"The Mensa 365 Brain Puzzlers Calendar" for 2001.
___________________________
Answer to Mini-MindBender for Kids
Four Digits
One logical solution path is as follows:
D can't be other than 1 because if D were 2 or more, D+B or D+C
would be more than 4. C must be 3. This is because if C were 4,
A would be 5; and if C were 2, no value for B makes D+B (1+B) equal
2. Therefore A is 4; B is 2; C is 3; D is 1. The addition is:
11
+23
---
34
This MindBender was modified from a puzzle in Norman D. Willis'
"The Little Giant Encyclopedia of Logic Puzzles."
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