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 14, 2002
MindBender
Two Brothers
Two brothers were born exactly one year apart. If you square their ages and then add those squares together, the total is 1105. How old are the two brothers?
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Mini-MindBender for Kids
Math Scramble
Unscramble the following math related words:
DAD MUS ROZE LAHF SLUP SINUM NITODIDA GEANEVIT GIDIT
CITSAAMTHEM TRASUCBT SIMET VIDDIE TRACIFON BUMNER
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...Answer to MindBender
Two Brothers
23 and 24. Use algebra to solve this MindBender:
X*X+(X+1)*(X+1)=1105
X*X+X*X+2*X+1=1105
2*X*X+2*X-1104=0
X*X+X-552=0
(X+24)*(X-23)=0
X=23 and X+1=24
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The MENSA Genius Quiz-A-Day Book."
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Answer to Mini-MindBender for Kids
Math Scramble
ADD SUM ZERO HALF PLUS MINUS ADDITION NEGATIVE DIGIT
MATHEMATICS SUBTRACT TIMES DIVIDE FRACTION NUMBER
This MindBender was modified from a puzzle in "Brain Games," a book by Dona Herweck Rice, et al.


October 17, 2002
Midweek MindBender
Nine-Letter Word
Can you think of a nine-letter word that contains only one vowel?
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...Answer to Midweek MindBender
Nine-Letter Word

STRENGTHS is one such word. There may be others. but I can't think of any more. Let me know if you can.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


October 21, 2002
MindBender
Fence Painting
If four people can individually paint a fence in 2, 3, 4, and 6 hours respectively, how long will it take them to paint the same fence if they all work together at their individual rates?
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Mini-MindBender for Kids
Defects
A product is produced with a 10 percent defect rate. If three of the products are selected at random, what are the chances that all three will be defective?
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...Answer to MindBender
Fence Painting
The number of fences each can paint in one hour are 1/2, 1/3, 1/4, and 1/6 respectively. The sum of those numbers (1/2+1/3+1/4+1/6) or 1.25 is the number of fences they can paint in one hour when working together. Therefore, the reciprocal of 1.25 is the number of hours it takes them to paint one fence if working together. 1/1.25=.8 hours or .8*60=48 minutes.
This MindBender was modified from a puzzle in Philip Carter and Ken Russell's "Power Puzzles 2."
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Answer to Mini-MindBender for Kids
Defects
One in one thousand chance. 1/10 * 1/10 * 1/10 = 1/1000.
This MindBender was modified from a puzzle in Philip Carter and Ken Russell's "Power Puzzles 2."


October 24, 2002
Midweek MindBender
Singular/Plural/Singular
Find four singular words that form their plural by adding "S" but if you add a second "S" they become singular again.
A four letter word meaning concern.
A six letter word that is a royal title.
A three letter word that is an undergarment.
An eight letter word that is a schedule of events.
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...Answer to Midweek MindBender
Singular/Plural/Singular

CARE CARES CARESS
PRINCE PRINCES PRINCESS
BRA BRAS BRASS
TIMELINE TILMELINES TIMELINESS
This MindBender was modified from a puzzle in the October 2002 issue of the Reader's Digest.


October 28, 2002
MindBender
Six Digit Addition
Each letter in this addition problem represents the same digit wherever it occurs. The digits used are 1, 2, 3, 4, and 5. What digit is represented by each letter?

AAE
EAC
____
BDD
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Mini-MindBender for Kids
Fraction Order
Order the following fractions from smallest to largest:
20/23 13/15 15/17 5/6
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...Answer to MindBender
Six Digit Addition
From the tens column, D must be 2 or 4. Since D is also the sum in the units column, D must be 4. Therefore, A equals 2. E and C must be 3 and 1, or 1 and 3. If E is 1, both B and C must be 3. This is impossible, so E is 3 and C is 1. Thus, B is 5. The total solution is:

223
321
____
544
This MindBender was modified from a puzzle in Norman D. Willis' "The Little Giant Encyclopedia of Logic Puzzles."
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Answer to Mini-MindBender for Kids
Fraction Order
Use a calculator or division to calculate decimal fractions to three decimal places. The correct order is:
.833 .866 .869 .882 or
5/6 13/15 20/23 15/17
This MindBender was modified from a puzzle in Summer 2002 issue of "The Original Logic & Math Puzzles" by Ebb Publications.


October 31, 2002
Midweek MindBender
Five-digit Number
Find a five-digit number that satisfies the following: the first digit is two more than the second; the second digit is two more than the third; the third digit is double the fourth; the fifth digit is half the fourth; and the sum of all digits is 21. The last condition is not really needed. Try solving it both with and without that condition.
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...Answer to Midweek MindBender
Five-digit Number

86421.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2003.


November 4, 2002
MindBender
Coins
If an A coin is worth 4 cents and a B coin is worth 7 cents, what bill amounts are impossible to pay with A and B coins only without getting any change?
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Mini-MindBender for Kids
Two Bugs
Two bugs were talking to each other. The first bug said to the second bug, "If you gave me two of your legs, we'd have the same number." The second bug replied, "If I had two of yours, I'd have three times as many legs as you." How many legs did each have?
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...Answer to MindBender
Coins
Bill amounts of 1, 2, 3, 5, 6, 9, 10, 13, and 17 cents cannot be made. Combine the following numbers of B coins with 0, 1, 2, etc. A coins:
O B coins: 0 4 8 12 16 20 24 28 32 36...
1 B coin: 7 11 15 19 23 27 31 35...
2 B coins: 14 18 22 26 30 34...
3 B coins: 21 25 29 33...
4 B coins: Same as part of 0 B coins.
5 B coins: Same as part of 1 B coins. And so on.
Notice that 1, 2, 3, 5, 6, 9, 10, 13, and 17 are the only numbers missing.
This MindBender was modified from a puzzle in David J. Bodycombe's book, "The Mammoth Puzzle Carnival."
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Answer to Mini-MindBender for Kids
Two Bugs
The first (F) had 6 legs. The second (S) had 10 legs.
F+2=S-2 or S=F+4
3*(F-2)=S+2 or 3*F=S+8
So 3*F=F+4+8 or 2*F=12
So F=6 and S=F+4=10
This MindBender was modified from a puzzle in Adam Hart-Davis' book, "Amazing Math Puzzles."


November 7, 2002
Midweek MindBender
Ten Pennies
Can you arrange ten pennies into five rows of four pennies each?
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...Answer to Midweek MindBender
Ten Pennies

Draw a five pointed star in the usual way without lifting your pen. Place a penny at each point of the star and at each line intersection.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.


November 11, 2002
MindBender
Tiresome Total
Below are a large number of individual digits all strung together. Can you quickly amd accurately determine the sum of all these individual digits?

1937556491285546372882191982734655732846
8264553782194637829155463782281937645528
7346558219375564912855463728821919827364
5573284682645537821946378291554637822819
3764552873465582193755649128554637288246
1982734655732846826455378219463782915573
3782281937645528734655821937556491285582
3728821919827346557328468264553782194637
8291554637822819376455287346558219375564
9128554637288219198273465573284682645528
8219463782915546378228193764552873465582
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Mini-MindBender for Kids
Random Digits
Can you determine an estimate for the sum of 1000 random digits?
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...Answer to MindBender
Tiresome Total
There are 11 lines with 40 digits on each line. Each pair of digits adds up to 10. Therefore, the total is: 40/2*10*11=2200.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Mindbending Puzzles."
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Answer to Mini-MindBender for Kids
Random Digits
The average value of a single digit is 4.5 which is calculated by ( (0+1+2+3+4+5+6+7+8+9)/10 ). Therefore, the sum of 1000 random digits is estimated at 1000*4.5 or 4500.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Mindbending Puzzles."


November 14, 2002
Midweek MindBender
Unusual Words
Can you determine what unusual feature the words ABSTEMIOUSLY and FACETIOUSLY have in common?
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...Answer to Midweek MindBender
Unusual Words

They both contain all the vowels in alphabetical order.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2002.


November 21, 2002
Midweek MindBender
Sister Ages
Fifteen years ago, Katie was one-third of Mary's current age. Ten years ago, Mary was twice what Katie's age was fifteen years ago. How old are they now?
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...Answer to Midweek MindBender
Sister Ages

Katie is 25. Mary is 30.
K-15=M/3=(M-10)/2
2M=3M-30 or M=30 so K=25.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


November 25, 2002
MindBender
Travel Distance
You start out on a driving trip. The first day you drive half the total distance. On the second day, you cover one third of the remaining distance. On the third day, you cover one third of the remaining distance. On the fourth day, you cover one half of the remaining distance. You now have 37 miles left to go. What distance have you traveled so far?
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Mini-MindBender for Kids
Letter Sequences
What letter should replace the "?" in the last sequence?
JFM
AMJ
JAS
O?D
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...Answer to MindBender
Travel Distance 
You have traveled 296 miles so far. Each day you cover, have 
so far covered, and have remaining the following fractions of 
the total trip: 
Day  Cover  So Far Covered  Remaining 
---  -----  --------------  --------- 
1     1/2        1/2           1/2 
2     1/6        2/3           1/3 
3     1/9        7/9           2/9 
4     1/9        8/9           1/9 
So 1/9 of the trip is 37 miles. So 8/9 of the trip is 8*37=296 miles.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Astounding Puzzles."
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Answer to Mini-MindBender for Kids
Letter Sequences
The missing letter is N. The letters are the initial letters of the twelve months.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Astounding Puzzles."


December 2, 2002
MindBender
Mixing
There is 1 liter of water in container A and 1 liter of milk in container B. You pour 1/2 liter of water from container A into B, mix thoroughly, and pour 1/4 liter of the mixture back into A. After mixing A's contents thoroughly, you pour 1/4 liter of A's mixture into B. Finally, after thoroughly mixing B's contents, you pour 1/2 liter from B into A. After all these operations, is there more milk in A than water in B?
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Mini-MindBender for Kids
Sum Fun
Use five index cards or five pieces of paper and do the following: on the first write "1" on one side and "2" on the other side; on the second write "3" on one side and "4" on the other side; on the third write "5" on one side and "6" on the other side; on the fourth write "7" on one side and "8" on the other side; on the fifth write "9" on one side and "10" on the other side. Have a friend lay these papers or cards down with either side facing up while you stand with your back turned and your eyes closed. Ask your friend to add up all the visible numbers, but not to tell you the total. Ask your friend how many odd numbers are visible. If you mentally subtract the number of odd numbers visible from 30, you can correctly determine the total that your friend calculated without ever seeing the numbers.
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...Answer to MindBender
Mixing
No calculations are needed for this MindBender. Containers A and B each hold the same amount of liquid after the operations as before them. Therefore, whatever milk A has acquired from B is equal to the amount of water B has acquired from A. So there is exactly as much milk in the water as there is water in the milk.
This MindBender was modified from a puzzle in Pierre Berloquin's book, "100 Numerical Games."
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Answer to Mini-MindBender for Kids
Sum Fun
This is just a fun game to play with your friends or parents so that you appear to be able to read minds. Watch for next week's Mini-MindBender for Kids to learn more about this game.
This MindBender was modified from a puzzle in Raymond Blum's book, "Mathemagic."


December 5, 2002
Midweek MindBender
Day vs. Year
Can you think of a place where a day is longer than a year?
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...Answer to Midweek MindBender
Day vs. Year

On the planet Venus, a day is longer than a year. Venus takes 243 Earth days to rotate on its axis (a Venus day) but it only takes 225 Earth days to go around the sun (a Venus year).
This MindBender was modified from a puzzle in Cliff Pickover's "Mindbending Puzzles" calendar for 2002.


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If you have any riddles or MindBenders to add please e-mail me or e-mail Mike Avery
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