MindBender Archive

Puzzles Archive
This is a list of the previous puzzles that have been sent out by E-mail.
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January 5, 1999
MindBender
Cryptarithmetic Addition
The following problem is a statement that many of us would make following the holidays. I just don't know whom we would ask to do the "sending."
A simple case of addition, where each of the letters S, E, N, D, M, O (the letter Oh), R, and Y uniquely represent one of the ten digits in the following cryptarithmetic problem in addition. The problem is best viewed in a mono-space font like Courier.
SEND
+ MORE
_______
MONEY
___________________________

Solve the above regular MindBender but use some of the following general tips for solving puzzles:
Use logical reasoning
Make an organized list
Use or look for a pattern
Brainstorm
Make a picture or diagram
Act out the problem or use objects
Make it simpler
Guess and check
Use or make a table
sdrawkcab kroW
___________________________

...Answer to MindBender
Cryptarithmetic Addition
9567
+ 1085
_______
10652
The above is the simple answer for this cryptarithmetic problem in addition. There are probably many methods of arriving at the final solution. The following are some of the steps in the thought processes I used to arrive at the solution:
The following are mostly based on consideration of addition and any carrying that occurs. Let a, b, c, and d represent the carrys from S+M, E+Oh, N+R and D+E respectively.
abcd the respective carry digit(0 or 1) from next column to the right
SEND
+ MORE
_______
MONEY
M equals 1 since that is the only carry possible with a two digit add. (a equals 1.)
S must be 8 or 9 and S + 1(M) + b must equal 10 since Oh can not be 1 (with S + 1(M) + b equal 11) because M already equals 1. Therefore, Oh equals 0.
If S is 8, then b is 1. E would then be 9 since E + 0(Oh) + c would produce a carry (b). This would mean N equals 0 which conflicts with Oh equals 0. So S equals 9. Therefore b equals 0.
N = E + 0(Oh) +c without producing a carry. Therefore, c equals 1.
N = E + 1
N + R + d = 10 + E
E + 1 + R + d = 10 + E
R + d = 9
R cannot be 9 since S is 9. Therefore, R equals 8 and d equals 1.
D + E produces a carry. So the only possibilities with the remaining digits are: 7+6, 7+5, 7+4, 7+3, 6+5, and 6+4.
7+3 would cause Y to be 0, but 0 is already used.
7+4 would cause Y to be 1, but 1 is already used.
6+5 would cause Y to be 1, but 1 is already used.
6+4 would cause Y to be 0, but 0 is already used.
7+6 with D=6 would cause N to be 8, but 8 is already used.
7+6 with E=6 would cause N to be 7, but 7 is already used.
7+5 with E=7 would cause N to be 8, but 8 is already used.
7+5 with E=5 and D=7 works and causes Y to be 2 and N to be 6.

January 7, 1999
FIFTH PSYCHIC GUESS
Abe, Bea, and Cal take the test with four aces and a joker. Flach card is correctly identified by at least one person. Nobodv gets two in a row correct, but everybody ends with the same numberr of right answers. What are the five cards?
...............1st Card.........2nd Card.........3rd Card..............4th Card
Abe.........Joker.............Heart..............Club..............Spade..............Diamond
Bea..........Club.............Joker.........Diamond..............Heart..............Club
Cal...........Spade.........Diamond............Spade..............Heart..............Joker

...The cards in order are: Spade, Joker, Club Heart Diamond.

January 11, 1999
A Different Sequence
Find the next number in the following different sequence:
14 15 16 20 22 24 32 112
___________________________

Mini-MindBender for Kids
Sam's Age
Sam's current age is a multiple of five. Next year Sam's age will be a multiple of seven. Sam is less than 50 years old. How old is Sam now?
___________________________

...Each number in the sequence is a representation of fourteen in a different base in descending order from base 10. This means that the next number is 1110 in base 2.
The only possibilities for Sam's age this year and next year based on the multiple of five requirement are:
This Year Next Year
0 1
5 6
10 11
15 16
20 21
25 26
30 31
35 36
40 41
45 46
The only one of those choices that is a multiple of seven next year is:
This Year Next Year
20 21
So Sam is currently 20 years old.

January 11, 1999
SIXTH PSYCHIC GUESS
Abe, Bea, Cal, and Dee guess at four aces and a joker. Each card is correctly identified by at least one person. Nobody gets them all right or all wrong. No two people make the same number of correct guesses. What are the five cards?
...............1st Card.........2nd Card.........3rd Card..............4th Card.........5th Card
Abe.........Club.............Joker..............Heart..............Diamond..............Club
Bea..........Diamond.............Joker.........Heart..............Club..............Spade
Cal...........Heart.........Club............Spade..............Diamond..............Joker
Dee...........Diamond.........Joker............Club..............Club..............Spade

...The cards in order are: Club, Joker, Heart, Diamond, Spade..

January 18, 1999
SEVENTH PSYCHIC GUESS
Abe, Bea, Cal, Dee, and Eb guess at four aces and a Joker. Each card is correctly identified by at least one person. At the conclusion, four persons are tied in the number correct guesses, with the fifth person having just one correct guess fewer. What are the five cards?
...............1st Card.........2nd Card.........3rd Card..............4th Card.........5th Card
Abe.........Club.............Joker..............Diamond..............Club..............Heart
Bea..........Joker.............Spade.........Club..............Spade..............Joker
Cal...........Club.........Club............Heart..............Diamond..............Joker
Dee...........Heart.........Diamond............Diamond..............Joker..............Club
Eb...........Spade.........Heart............Joker..............Spade..............Diamond

...Club. Heart, Diamond, Spade, Joker

January 18, 1999
New Math
A friend tells you that he has been working with a new kind of arithmetic. He says that in his arithmetic, "one-half of five equals three." If this is so, what would a third of ten be in this new math? Show your work, don't just guess!
___________________________
Mini-MindBender for Kids
Double Letters
In going over the books one day, a bookkeeper noticed that the word "balloon" had two sets of double letters ("lloo") one right after the other. "I wonder," he said to himself, "if there is an English word that contains three sets of double letters, one right after the other." Can you think of such a word?

...Assume that the "New Math" is based upon a factor applied to "Old Math." Let the factor be K. Then the following shows my work:
1/2 * 5 * K = 3
5 * K = 6
K = 1.2
1/3 * 10 * K =
1/3 * 10 * 1.2 = 4
So a third of ten is four in this "New Math."

Answer to Mini-MindBender for Kids
Double Letters
The word is "bookkeeper" and it was right in front of you.
This Mini-MindBender was modified from a puzzle in Martin Gardner's book, "The Unexpected Hanging and Other Mathematical Diversions."

January 22, 1999
EIGHTH PSYCHIC GUESS
Abe, Bea, Cal, Dee, Eb, and Flo take the test using four aces. Although nobody gets all answers right, there is a clear winner. Two people are tied for second-best score, and two others are tied for third-best score. What are the four cards?
...............1st Card.........2nd Card.........3rd Card..............4th Card
Abe.........spade.............spade..............Club..............Diamond
Bea..........Heart.............Diamond.........Diamond..............Club
Cal...........Dimaond.........Club............Heart..............Spade
Dee...........Diamond.........Heart............Spade..............Club
Eb...........Heart.........Spade............Club..............Dimaond
Flo...........Club.........Spade............Diamond..............Heart

...The cards in order are: Heart, Spade, Diamond, Club

January 25, 1999
NINTH PSYCHIC GUESS
Abe, Bea, Cal, Dee, and Eb guess at four aces and a joker, Each card is correctly identified by at least one person. All five people make the same number of corrert guesses. What are the five cards?
...............1st Card.........2nd Card.........3rd Card..............4th Card..............5th Card
Abe.........spade.............Heart..............Club..............Joker..............Diamond
Bea..........Sapde.............Joker.........Diamond..............Club..............Spade
Cal...........Club.........Diamond............Spade..............Joker..............Heart
Dee...........Diamond.........Heart............Joker..............Club..............Spade
Eb...........Club.........Joker............Diamond..............Spade..............Heart

...The Cards in order: Club, Heart, Diamond, Joker Spade.
These puzzles were from Roger Huffordís book ìChallenging Puzzles in Logic (Dover Books, 1982)

February 9, 1999
In a certain small high school the courses in Biology, Economics, English, French, History, and Mathematics are taught by just three men, Mitchell, Morgan, and Myers, each of whom teaches two subjects.
The economics teacher and the French teacher are next-door neighbors.
Mitchell is the youngest of the three.
The men ride to and from school together, Myers, the Biology teacher, and the French teacher each driving one week out of three.
The Biology teacher is older than the Mathematics teacher.
When they can find a fourth, the English teacher, the mathematics teacher, and Mitchell usually spend their lunch hour playing bridge.
What subjects does each man teach?

...oldest...Morgan taught Biology & English
Middle..Myers taught Economics & Math
Youngest...Mitchell taught French & History

February 10, 1999
Liars
Harry lies on Monday, Tuesday, and Wednesday. Terry lies on Thursday, Friday, and Saturday. At all other times, Harry and Terry tell the truth.
"Yesterday was one of my lying days," says Harry.
"Yesterday was one of my lying days too," says Terry.
What day of the week is it?
___________________________
Mini-MindBender for Kids
Typing
Find a word of ten letters that can be typed using only the top row of letters on a typewriter.
___________________________

...Answer to MindBender
Liars
This answer is best viewed in a mono-space font like Courier.
Thursday.
Look at the following chart for Monday through Sunday and consider the statements of Harry and Terry and look at each day and each day's predecessor.
.........Sun... Mon... Tue... Wed... Thu... Fri... Sat... Sun
Harry...T ..... L ...... L ....... L ..... T .... T ... T .... T
Terry...T ..... T ...... T ...... T ...... L .... L .... L ... T
The only day that works is Thursday.
This MindBender was modified from a puzzle in Harold R. Jacob's book, "Mathematics - A Human Endeavor."
___________________________
Answer to Mini-MindBender for Kids
Typing
TYPEWRITER
This Mini-MindBender was modified from a puzzle in Martin Gardner's book, "The Unexpected Hanging and Other Mathematical Diversions."

February 15, 1999
Church Theft
A church safe was broken into and the Sunday offering was stolen. Four suspects were identified. Each suspect made one statement. Three of the suspects told the truth and the guilty suspect lied. Who stole the church's money?
Sonny: Beatrice is lying.
Andy: I was not in town at the time of the theft.
Zoli: Sonny's telling the truth.
Beatrice: Sonny is the guilty one.
___________________________
Mini-MindBender for Kids
3 Golfers
Three golfers named Terry, Kris, and Sam are walking single file back to the clubhouse after a game of golf. Terry, the best golfer of the three, always tells the truth. Kris sometimes tells the truth, while Sam, the worst golfer, never tells the truth.
The following are the statements by the three golfers as they walk single file:
First Golfer: The golfer directly behind me is Sam.
Second Golfer: My name is Kris.
Third Golfer: The golfer directly in front of me is Terry.
Determine the names of the first, second, and third golfers.
___________________________

...Answer to MindBender
Church Theft
Beatrice is the guilty one. If three people are telling the truth, then since Sonny says Zoli is telling the truth and Beatrice says that Sonny did it, Beatrice is the one telling the lie. Since the one lying was the thief, Beatrice must be the thief.

OR

Sonny and Beatrice cannot both be telling the truth since their statements are in conflict. Therefore, Zoli is telling the truth and he says that Sonny is telling the truth. Therefore, Beatrice is lying and is the guilty one.
___________________________
Answer to Mini-MindBender for Kids
3 Golfers
The third golfer cannot be Terry since Terry always tells the truth and the third golfer says that the second golfer is Terry. The second golfer cannot be Terry since Terry always tells the truth and the second golfer says that the second golfer is Kris. Therefore, the first golfer is Terry.
Therefore, since the first golfer says that Sam is immediately behind, and the first golfer (Terry) always tells the truth, the second golfer is Sam.
Therefore, the third golfer is Kris. (Kris was lying this time when he said, "The golfer directly in front of me is Terry.")
This MindBender was modified from a puzzle in Harold R. Jacob's book, "Mathematics - A Human Endeavor."

February 22, 1999
Fermat Claim
A man claims that he has found a couter example to Fermat's last theorem. He says that:
1324**N + 731**N = 1961**N
for some value of N but he refuses to disclose the value of N. How do you know that he is mistaken?
___________________________
Mini-MindBender for Kids
Sum Equals Product
What three positive integers when added together equal the same three positive integers when multiplied together?
___________________________

...Answer to MindBender
Fermat Claim
1324 raised to any power, N, ends in either 4 (odd values of N) or 6 (even values of N). The other two numbers, 731 and 1961, raised to any power must each end in 1. Since any number ending in 4 or 6 added to a number ending in 1 will result in a number ending in 5 or 7, the equation:
1324**N + 731**N = 1961**N
has no solution.
This MindBender was modified from a puzzle in Martin Gardner's book, "Wheels, Life and Other Mathematical Amusements."
___________________________
Answer to Mini-MindBender for Kids
Sum Equals Product
1 + 2 + 3 = 1 * 2 * 3
This is the only solution.
This MindBender was modified from a puzzle in Martin Gardner's book, "Wheels, Life and Other Mathematical Amusements."

March 1, 1999
MindBender
12300
Consider the following addition problem:
ABCD
+DCBA
+WXYZ
_________
12300
Where A, B, C, and D are four consecutive digits in increasing order and D, C, B, and A are the same four digits in decreasing order. W, X, Y, and Z are the same four digits in an unknown order. Determine the number WXYZ.
___________________________
Mini-MindBender for Kids
Six Letters
This problem is best viewed in a mono-space font like Courier.
In the following line of letters eliminate six letters so that the remaining letters, without changing their order, spell a familiar English word.
B S A I N X L E A T N T E A R S
___________________________

...Answer to MindBender
12300
If ABCD = 1234, it is not possible to get an answer as large as 12300.
If ABCD = 3456 or larger, it is not possible to get an answer as small as 12300.
Therefore, ABCD = 2345; DCBA = 5432; and WXYZ = 4523.
2345
+5432
+4523
_________
12300
This MindBender was modified from a puzzle in Martin Gardner's book, "Wheels, Life and Other Mathematical Amusements."
___________________________
Answer to Mini-MindBender for Kids
Six Letters
Two Answers:
1. Eliminate "S I X L E T T E R S" leaving BANANA.
Or
2. Eliminate all occurrences of the six letters S, A, I, N, X, and L leaving BETTER.
This Mini-MindBender was modified from a puzzle in Martin Gardner's book, "The Unexpected Hanging and Other Mathematical Diversions."

March 8, 1999
MindBender
What Day
A vacationing family sitting around the campfire has the following conversation:
Father: What day is it? I am sure it isn't Tuesday, Wednesday or Thursday.
Mother: Well that's not very helpful, dear. Besides yesterday was Friday.
Father: No, now that I think about it, yesterday wasn't Friday, tomorrow is Friday.
Junior: The day after tomorrow is Thursday.
Susie: You are nuts. Tomorrow is Thursday.
Mother: Actually, it's probably Thursday today.
Junior: All we know for sure is that it wasn't Sunday yesterday.
If only one statement above is true, what day of the week is it?
___________________________
Mini-MindBender for Kids
Sixty Cents
The following is a conversation in a hardware store:
Customer: "How much will one cost?"
Clerk: "Twenty cents."
Customer: "How much will twelve cost?"
Clerk: "Forty cents."
Customer: "I'll take nine hundred and twelve."
Clerk: "That will be sixty cents."
What was the customer buying?
___________________________

...Answer to MindBender
What Day
To help solve the puzzle, number each statement and write down the list of days that it could be assuming each statement is true.
1) Monday, Friday, Saturday, Sunday
2) Saturday
3) Thursday
4) Tuesday
5) Wednesday
6) Thursday
7) Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
The only day mentioned one time is Monday. Therefore it must be Monday, otherwise more than one of the statements would be true.
Alternate and Equivalent Solution:
This solution is best viewed in a mono-space font like Courier.
Make a chart of the truth of the seven statements on each day of the week.
The only day with only one true statement is Monday.
Mon Tue Wed Thu Fri Sat Sun
1) T F F F T T T
2) F F F F F T F
3) F F F T F F F
4) F T F F F F F
5) F F T F F F F
6) F F F T F F F
7) F T T T T T T
___________________________
Answer to Mini-MindBender for Kids
Sixty Cents
House numbers.

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