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.


December 3, 2001
MindBender
Rope Order
The clerk misunderstood the customer's rope order. He reversed feet and inches and the customer only got 30% of what he ordered. How much rope had the customer originally ordered if no fractional inches were involved?
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Mini-MindBender for Kids
Math Problems
You start out on the first day working math problems. That day you do 20 math problems. Practice at working the problems makes you much faster at doing them. Each day, after that first day, you are able to do 15 more problems than you did the day before. How many days does it take you to do 250 problems altogether?
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...Answer to MindBender
Rope Order
Algebra gets us part way. Let F be the number of feet originally ordered and I be the original number of inches ordered.
0.3*(12F+I)=12*I+F
3.6*F+0.3*I=12*I+F
2.6*F=11.7*I
F=4.5*I
Both F and I must be less than 12 or the clerk could not have confused the order. I must be even so that F can be a whole number. If I is 4 or larger, F is greater than 12. So I must be 2 and F must be 9. The original order was for a rope that was 9 feet 2 inches long. The customer got a rope that was 2 feet 9 inches long.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.
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Answer to Mini-MindBender for Kids
Math Problems
The numbers of problems done on successive days are 20, 35, 50, 65, 80, and so on. The total numbers of problems worked on successive days are 20, 55, 105, 170, 250, and so on. Therefore it takes 5 days to work a total of 250 math problems.
The MindBender moderator is the source for this Mini-MindBender.


December 6, 2001
Midweek MindBender
Word Path
The following matrix of nine letters spells out a word. Find a path from letter to letter that spells out the word. Each letter is used only once.

C E T
L A A
C U L
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...Answer to Midweek MindBender
Word Path

The word is CALCULATE. Start in the top, left corner.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.


December 10, 2001
MindBender
Four Sisters
Four sisters (Kris, Terri, Mary, and Suzie) are musicians and also fluent in four languages. Each plays a different musical instrument (the clarinet, flute, piano, and violin) and each speaks a different language (German, French, Spanish, and Italian). From the following statements, which sister plays which instrument and which sister speaks which language?
1. The sister who plays the clarinet does not speak French or German.
2. The sister who speaks Spanish cannot carry her instrument to her lessons.
3. Mary doesn't speak German or Spanish, nor does she play the clarinet.
4. Kris is not the sister who speaks German.
5. Neither Suzie (who doesn't play the flute) nor Kris plays the clarinet.
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Mini-MindBender for Kids
Train Tunnel
A train that is 1/8 of a mile long is travelling at 30 miles per hour and is about to enter a tunnel that is 6 1/2 miles long. How long will it take the whole train to pass through the tunnel, from when the front of the train enters the tunnel until the rear of the train emerges from the tunnel?
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...Answer to MindBender
Four Sisters
From statements 1 and 2, the sister who plays the clarinet speaks Italian, and the one who speaks Spanish plays the piano. From statement 3, Mary must be the sister who speaks French, and she plays either the violin or the flute. From statements 4 and 5, Kris speaks Spanish and plays the piano, and Terri must be the sister who plays the clarinet and speaks Italian. Therefore, it is Suzie who plays the violin and speaks German, and Mary plays the flute. The whole answer is:
Kris: Piano / Spanish
Terri: Clarinet / Italian
Mary: Flute / French
Suzie: Violin / German
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
Train Tunnel
When the front of the train enters the tunnel, the rear of the train is 1/8 mile behind. So the rear of the train must travel the length of the tunnel plus the length of the train. That number of miles (6.5+0.125) divided by the speed of the train in miles per hour results in the number of hours it takes the train to completely pass through the tunnel. Multiplying that result by 60 minutes per hour, results in the number of minutes it takes. In minutes, the total time is (6.5+0.125)/30*60 = 13.25 minutes or 13 minutes and 15 seconds.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Astounding Puzzles."


December 13, 2001
Midweek MindBender
Word
Use the following rhyme to determine the five-letter word that spells the answer to the riddle.
My first is in bring but not in fry.
My second in ring but not in high.
My third in over but not in near.
My fourth in open but not in hear.
My last in lock but not in lean.
My whole a charming landscape scene.
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...Answer to Midweek MindBender
Word

BROOK
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


December 17, 2001
MindBender
Dice Chance
You roll two dice and they total 6. What are the chances that you will roll a 6 again before you roll a 7? If you roll any number other than 6 or 7, you just ignore that roll and roll again until either 6 or 7 comes up. Both dice are normal playing dice with six faces numbered 1 through 6.
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Mini-MindBender for Kids
Planets
The names of all nine planets are hidden in the matrix of letters below. Can you find all nine of them? Look up, down, sideways, and diagonally. Some overlap and some are backwards. 
L M V E N U S O 
R O E E A R T H 
E S M R K A F P 
T A O A C N L R 
I T A P R U U R 
P U P L T S R E 
U R M O O O N Y 
J N E P T U N E
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...Answer to MindBender
Dice Chance
5 in 11. There are 5 ways to roll a 6 (1-5, 2-4, 3-3, 4-2, 5-1) and 6 ways to roll a 7 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1). Together there are 11 ways to determine the outcome. Of those 11 ways, five of them are 6. So the chances are 5 in 11.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.
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Answer to Mini-MindBender for Kids
Planets
The answers are shown by lower case for the nine planets. 
L m v e n u s O 
r O e e a r t h 
e s m r K a F p 
t a O a c n l R 
i t A P r u U R 
p u P L t s r E 
u r M o O O N y 
j n e p t u n e
This MindBender was modified from a puzzle in Highlights "Puzzlemania," a good thinking resource for young kids.


December 20, 2001
Midweek MindBender
Stamps
Tony had a stamp collection. Tony didn't have many stamps, but they were first class. Tony sold one-half of the stamp collection one week, 25 stamps the next week, one-fourth of the original number of stamps the third week. Tony then had 20 stamps left. How many stamps did Tony have to begin with?
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...Answer to Midweek MindBender
Stamps

180.
X-X/2-25-X/4=20
X/4=45
X=180
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


December 24, 2001
MindBender
Series
Fill in the two missing terms in the following series: Q1A ??? S4D T8F U16G V32H W64J ??? Y256L
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Mini-MindBender for Kids
Bush Height
You plant a bush in your yard in March. It doubles in height every month. After six months it is 12 feet high. During what month did it reach 3 feet?
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...Answer to MindBender
Series
The missing terms are R2S and X128K. The first item in each term is the letters in sequence from Q. The second item is successive powers of 2. The third item is the letters from the second row of a standard keyboard.
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
Bush Height
July. In September (six months after March), it is 12 feet high. In August, it is 6 feet high. So in July, it is 3 feet high.
This MindBender was modified from a puzzle in Victor Serebriakoff's book, "The Mammoth Book of Mindbending Puzzles."


December 27, 2001
Midweek MindBender
Series
What is the next number in the following series?
62/93, 77/132, 0.5, 115/276, 0.33333..., a quarter, 1/6, ??
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...Answer to Midweek MindBender
Series

1/12. Another view of this series is:
8/12, 7/12, 6/12, 5/12, 4/12, 3/12, 2/12, 1/12
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


December 31, 2001
MindBender
Impostor
An impostor's identity is being investigated. The impostor is known to be one of three people: A, B, or C. The three people make the following statements:
A: C is the impostor.
A: B's first statement is true.
B: I am not the impostor.
B: A is the impostor.
C: A's second statement is true.
C: B's second statement is false.
If it is known that the impostor makes one true and one false statement and the truthfulness of the other two suspects is unknown, who is the impostor?
___________________________

Mini-MindBender for Kids
Ghosts
Guests at a hotel have reported seeing ghosts in room F and in room S. In January, 7 ghosts were reported in room F and 7 in room S. In February, there were 12 reports for room F and 9 reports for room S. In March, 11 ghosts were reported in room F and 12 ghosts were reported in room S. In April, there were 16 reports for room F and 14 reports for room S. If the reports continued according to this pattern, what would be the next month that the same number of ghosts would be reported in both room F and room S?
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...Answer to MindBender
Impostor
If B were the impostor, both of B's statements would be false. Therefore, B must not be the impostor. If C were the impostor, both of C's statements would be true. Therefore, C must not be the impostor. So A is the impostor and A's first statement is false and A's second statement is true.
This MindBender was modified from a puzzle in Norman D. Willis' "The Little Giant Encyclopedia of Logic Puzzles."
___________________________

Answer to Mini-MindBender for Kids
Ghosts
August. The reports in room F go up by 5 and then down by 1, and then repeat that pattern. The reports in room S go up by 2 and then up by 3, and then repeat that pattern. The following lists the number of reports for each room by month: 
       Jan Feb Mar Apr May Jun Jul Aug 

Room F   7  12  11  16  15  20  19  24 

Room S   7   9  12  14  17  19  22  24
This MindBender was modified from a puzzle in "The Problem Solver 4" by Judy Goodnow and Shirley Hoogeboom.


January 3, 2002
Midweek MindBender
Five Words
Below are five words that can become five different words when the same three letters are added to the beginning of each word. What are the three letters that will do this? SHY VAIL DING IT DUCE
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...Answer to Midweek MindBender
Five Words

TRA added to the beginning of each word results in: TRASHY TRAVAIL TRADING TRAIT TRADUCE
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


January 7, 2002
MindBender
If
If 3 were -11 how much would -9 be?
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Mini-MindBender for Kids
Definition
What is the meaning of the word lenitive?
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...Answer to MindBender
If
3/(-11) = (-9)/X Cross multiply to get: 3X = 99 or X = 33
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.
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Answer to Mini-MindBender for Kids
Definition
Lenitive means lessening pain or distress.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


January 10, 2002
Midweek MindBender
Where for 9 and 10
Here's an odd puzzle, even though you may not agree. Where should the numbers 9 and 10 be placed, above or below the line?
1 2 3 6 7 8
_____________
0 4 5
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...Answer to Midweek MindBender
Where for 9 and 10

9 goes below the line; 10 goes above the line. The hint in the question was the use of the words even and odd. The numbers above the line have an odd number of letters in the spelling of their names. Below the line, the names have an even number of letters.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


January 14, 2002
MindBender
Word Sequence
Which of the words ANSWER, ALWAYS, WHISPER, or MINUS completes the following sequence? ZEBRA RAMBLE LEGAL ????
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Mini-MindBender for Kids
Long Word
Fill in the blanks top complete the following word: B--K--E--R
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...Answer to MindBender
Word Sequence
ALWAYS. Each word in the sequence starts with the last two letters of the previous word. There may be other logical answers also.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.
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Answer to Mini-MindBender for Kids
Long Word
BOOKKEEPER
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


January 17, 2002
Midweek MindBender
Added Factors
The first number whose factors add up to more than the number itself (disregarding the number itself as a factor) is 12, where the factors are 1, 2, 3, 4, 6. What are the next three numbers whose factors add to more than themselves?
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...Answer to Midweek MindBender
Added Factors

18 (1, 2, 3, 6, 9) 20 (1, 2, 4, 5, 10) 24 (1, 2, 3, 4, 6, 8, 12)
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


January 21, 2002
MindBender
Candy
Candy in a package needs to be divided equally among 3, 4, 5, or 7 people. What is the least number of pieces of candy that can be in the package?
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Mini-MindBender for Kids
Octopus
Octopus is to 8 as Squid is to what?
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...Answer to MindBender
Candy
420. This is the least common multiple of 3, 4, 5, and 7. 420 = 3*4*5*7.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.
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Answer to Mini-MindBender for Kids
Octopus
10. A squid has 10 tentacles.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.


January 24, 2002
Midweek MindBender
Ages
Will is now one-half Beth's age. Six years ago, he was one-fourth Beth's age. How old are they now?
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...Answer to Midweek MindBender
Ages

Will is 9. Beth is 18.
W=B/2
W-6=(B-6)/4
B/2-6=(B-6)/4
(B-12)/2=(B-6)/4
4B-48=2B-12
2B=36
B=18
W=B/2=18/2=9
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


January 28, 2002
MindBender
Pizzas
If six and a half boys can eat six and a half pizzas in an hour and a half, how many pizzas could eight boys eat in seven and a half hours?
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Mini-MindBender for Kids
Rabbit Weight
While in a pet store, the owner tells you that a rabbit weighs ten pounds plus half its own weight. How much does the rabbit weigh?
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...Answer to MindBender
Pizzas
40. From the assumption, each boy can eat one pizza in an hour and a half or five pizzas in seven and a half hours (7.5/1.5=5) and 8*5=40.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2002.
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Answer to Mini-MindBender for Kids
Rabbit Weight
20 pounds. Let R be the rabbit's weight. Then Algebra shows us:
R = 10 + R/2
R/2 = 10
R = 20
This MindBender was modified from a puzzle in Cliff Pickover's "Mindbending Puzzles" calendar for 2002.


January 31, 2002
Midweek MindBender
Letter Sequence
What is the next letter in the following sequence? Hint: Regardless of when you solve this, it will be just in time.
S M H D W M ?
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...Answer to Midweek MindBender
Letter Sequence

Y. These are the first letters of the following increasing units of time: Second Minute Hour Day Week Month Year.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


February 4, 2002
MindBender
Profit or Loss
You buy two different 14K gold pieces of jewelry. You later need to sell them both to get enough money to pay taxes. You sell each of them for $600, one at a loss of 25% and one at a profit of 25%. Overall did you gain or lose money on the two deals together? Try to answer this at first without doing any calculations.
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Mini-MindBender for Kids
Piggy Bank
Alex puts 36 cents ($0.36) into his piggy bank every day. If his piggy bank were empty to start with, how many days does it take until his bank contains a whole number of dollars (no cents) and how many dollars will then be in Alex's piggy bank?
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...Answer to MindBender
Profit or Loss
You lost money on the deal because the loss was 25% of an amount larger than $600 and the gain was 25% of an amount smaller than $600. The original prices of the two pieces of jewelry were 600/.75=800 and 600/1.25=480. So you lost $200 and gained $120 for a combined loss of $80.
The MindBender moderator is the source for this MindBender.
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Answer to Mini-MindBender for Kids
Piggy Bank
25 days and nine dollars. Start with zero and keep adding 36 until a total that ends in 00 is the result. This takes 25 additions of 36 and the total is 900. So it takes 25 days and the total is $9.00 in the bank.
This MindBender was modified from a puzzle in Highlights "Mathmania," a good thinking resource for young kids.


February 7, 2002
Midweek MindBender
Added Word
What three letter word can be added to the beginning of
___KING
___DON
___TAKE
to make three new words?
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...Answer to Midweek MindBender
Added Word

PAR to make PARKING PARDON and PARTAKE.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2002.


February 11, 2002
MindBender
Logical Words
The following words follow a logical progression: ACE TAB COG ADD EAR RAF GUT UGH IVY TAJ. Which of these words could be next? KID BOY ASK TOO
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Mini-MindBender for Kids
Hidden Coins
Three kids, Alex, Max, and Will, are each holding some number of coins behind their backs. You ask each of them how many they are holding. They refuse to say, but do tell you that Alex and Max together hold three coins; Alex and Will together hold five coins; and Max and Will together hold four coins. How many coins do each of them hold?
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...Answer to MindBender
Logical Words
KID. The words begin with A, end with B, begin with C, end with D...
This MindBender was modified from a puzzle in Pierre Berloquin's book, "100 Games of Logic."
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Answer to Mini-MindBender for Kids
Hidden Coins
Solve with three equations in three unknowns or consider the following: 3+5+4=12 is the number of coins held by Alex, Max, Alex, Will, Max, and Will together. In other words since each name is mentioned twice, 12 is twice the total number of coins or the total number of coins is 6. Since Alex and Max together hold 3, Will must hold 3 by himself. Therefore, Max holds 1 coin and Alex holds 2 coins.
The MindBender moderator is the source for this Mini-MindBender.


February 14, 2002
Midweek MindBender
Next Number
What is the next number in the following sequence:
2 6 12 48 96 480 960 5760 11520 ??
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...Answer to Midweek MindBender
Next Number

80640. The numbers are multiplied by 3, 2, 4, 2, 5, 2, 6, 2, and 7.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.


February 18, 2002
MindBender
Missing Number 
What is the missing number indicated by X? 

   9         4 
 |---|     |---| 
7| 4 |6   7| 9 |9 
 |---|     |---| 
 
 
   7         5 
 |---|     |---| 
7| 9 |5   4| 3 |X 
 |---|     |---|
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Mini-MindBender for Kids
Emily's Sore Feet
Emily's feet are sore. She and Sam had walked a total of 12 miles in the Bishop School Walk-a-thon. Emily had walked twice as far as Sam. How many miles did Emily and Sam each walk? Use guessing and checking to find an answer.
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...Answer to MindBender
Missing Number
5. The numbers in the same position in each of the boxes always add up to 25.
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
Emily's Sore Feet
Guess 7 for the number of miles Emily walked. Then Sam would have walked 1/2 of 7 or 3.5 miles. The combined total would only be 10.5. This isn't enough, so try a new guess for Emily's miles. Guess 8 miles for Emily. Then Sam would have walked 1/2 of 8 or 4 miles. The combined total would be 8+4 or 12. This is correct. So Emily walked 8 miles and Sam walked 4 miles.
This MindBender was modified from a puzzle in "The Problem Solver 4" by Judy Goodnow and Shirley Hoogeboom.


February 20, 2002
Midweek MindBender
Historic Minute
Tonight at 8:02 PM will be a historic minute. Something will happen which has not occurred for many years and will seldom happen again. What is that significant happening?
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...Answer to Midweek MindBender
Historic Minute

As the clock ticks over from 8:01 PM on Wednesday, February 20, time will, for sixty seconds only, read in perfect symmetry 2002, 2002, 2002, or to be more precise - 20:02, 20/02, 2002. The last occasion that time read in such a symmetrical pattern was long before the days of the digital watch and the 24-hour clock - at 12:21 PM on December 21, 1221. And because the clock only goes up to 23:59, it is something that will only happen again in 2112. The following years also work (the first three if you accept leading zeros in the year) with either E for European dates (ddmm), U for USA dates (mmdd), or B for both:
0110 B
0220 U
0330 U
1001 B
1111 B
1221 U
2002 E
2112 E
This MindBender was modified from a note from one of our MindBender Solvers. I also saw it earlier today. It probably can be seen frequently on the Internet today.


February 25, 2002
MindBender
Painting Togetherness
If Matt can paint a small room in three hours and Terri can paint the same room in two hours, how long will it take them to paint the room if they work together?
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Mini-MindBender for Kids
Cycles
You are on the playground and are happy to see both bicycles (two wheels) and tricycles (three wheels). You count the wheels and come up with a total of 12. How many bicycles and how many tricycles are there on the playground?
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...Answer to MindBender
Painting Togetherness
Matt paints 1/3 of the room each hour (the inverse of 3). Terri paints 1/2 of the room each hour (the inverse of 2). Together they paint 1/2 + 1/3 or 5/6 of the room each hour. At that combined rate it takes them 6/5 hours to paint the room together (the inverse of 5/6). So it takes Matt and Terri one hour and 12 minutes to paint the room together.
This MindBender was modified from a puzzle submitted by Eric, one of the MindBender solvers.
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Answer to Mini-MindBender for Kids
Cycles
There must be an even number of tricycles for the total number of wheels to be even. If there are four tricycles, there are 12 wheels and no wheels left for bicycles. So there must be two tricycles and three bicycles. Another way is to consider the possibilities: NP means "Not Possible to choose a number to make the total 12." 
Tricycles Bicycles 
    1        NP 
    2        3 
    3        NP 
    4        NP (zero)
This MindBender was modified from a puzzle in Adam Hart-Davis' book, "Amazing Math Puzzles."


March 4, 2002
MindBender
Race
In a race, Dave beat Frank. Carol was not last, but she beat Bob. Elly lost to Bob, but she beat Dave. Who was last?
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Mini-MindBender for Kids
No Vowels
All the vowels (even Y) have been removed from the following line in a nursery rhyme. Can you read it?
MSTRSSMRQTCNTRRHWDSRGRDNGRW
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...Answer to MindBender
Race
Frank. The final order was Carol, Bob, Elly, Dave, Frank.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2002.
___________________________

Answer to Mini-MindBender for Kids
No Vowels
Mistress Mary, quite contrary, how does your garden grow?
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "365 Brain Puzzlers" Calendar for 2002.


March 7, 2002
Midweek MindBender
Sand and Rock
Sand costs $40 per ton and rock costs $60 per ton. How many tons of sand and how many tons of rock must be combined to make 300 tons of a sand-rock mix that is to be sold at $45 per ton?
___________________________

...Answer to Midweek MindBender
Sand and Rock

Solve the following algebraic equation where S is the tons of sand: 40*S + 60*(300-S) = 45*300 to arrive at the answer of 225 tons of sand and 75 tons of rock.
The MindBender moderator is the source for this Midweek MindBender.


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