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.


August 20, 2001
MindBender
495 Sum
How many ways can you use the digits 1,2,3,6,7,and 8 to form two 3-digit numbers that add to a total of 495. The addition would then use all the digits from 1 to 9, once each. Do not consider reversing the two addends as separate answers.
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Mini-MindBender for Kids
Video
An item at a store costs $5.50 including tax. If the item cost $5.00 more than the tax, how much was the item and how much was the tax?
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...Answer to MindBender
495 Sum

3 and 1 must be the hundreds digits in the two addends. Then 8 and 7 must be the units digits in the two addends. That leaves 2 and 6 for the tens digits. This results in the following possible sums: 127+368=495. 168+327=495; 128+367=495; 167+328=495

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
Video
The item cost $5.25 and the tax was $0.25. If you got $5.00 for the item and $0.50 for the tax, try again.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


August 27, 2001
MindBender
Challenger
Fill each square with a number, 1 through 9 (duplicates allowed). Rows should add to totals on the right. Columns should add to totals on the bottom. Diagonals through the center (C) should add to totals in the upper right and lower right. There may be more than one solution. 
                    ______ 
                    | 22 | 
__________________________ 
|  2 |    |    |    | 17 | 
__________________________ 
|    |    |    |  4 | 24 | 
__________C_______________ 
|    |  7 |    |    | 28 | 
__________________________ 
|    |    |  9 |    | 22 | 
__________________________ 
| 14 | 31 | 30 | 16 | 22 | 
__________________________
___________________________

Mini-MindBender for Kids
Upset Age
Mary is somewhat upset about her age so she won't say how old she is. She does say that she is three times as old as she will be in 5 years less 3 times as old as she was 5 years ago. How old is Mary?
___________________________
...Answer to MindBender
Challenger

I started with the middle two columns as they had the highest totals. Then I worked on rows 1 and 4, and then the diagonals, making any necessary adjustments as I went along to keep the totals correct. The answer I came up with was the same as the newspaper's answer. 
                    ______ 
                    | 22 | 
__________________________ 
|  2 |  8 |  3 |  4 | 17 | 
__________________________ 
|  3 |  8 |  9 |  4 | 24 | 
__________C_______________ 
|  7 |  7 |  9 |  5 | 28 | 
__________________________ 
|  2 |  8 |  9 |  3 | 22 | 
__________________________ 
| 14 | 31 | 30 | 16 | 22 | 
__________________________
This MindBender was modified from a puzzle in the Des Moines Register.
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Answer to Mini-MindBender for Kids
Upset Age
Simple algebra lets us solve this problem easily. Let Mary's age be M. Then we have
M = 3*(M+5) - 3*(M-5) or
M = 3*M +15 -3*M +15 or
M = 30 so Mary is 30 years old.
The MindBender moderator is the source for this Mini-MindBender.


September 3, 2001
MindBender
Subtraction
In the following subtraction, A, B, C, and D are 2, 4, 6, and 8 in some order. What is the subtraction problem using digits and not letters? 
 ABC 
-BDB 
_____ 
 DDB
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Mini-MindBender for Kids
Series
What is the next number in the following six number series? Choose your answers from 1 4 9 13 16 45. Use each of those numbers as the answer to only one series.
Series A: 1 3 5 7
Series B: 21 16 11 6
Series C: 9 11 10 12 11
Series D: 1 2 4 8
Series E: 5 15 25 35
Series F: 4 3 4 3
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...Answer to MindBender
Subtraction

There can be no borrows or some odd digits would occur. Therefore, since 2*D=B and 2*B=C, B and D must be 4 and 2 respectively. So C is 8 and A is 6. The complete answer is: 
 648 
-424 
_____ 
 224
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
Series
The following answer includes my reasons. Others may also work.
Series A: 1 3 5 7 9 (odd numbers)
Series B: 21 16 11 6 1 (decreasing by 5)
Series C: 9 11 10 12 11 13 (up 2, down 1, up 2, down 1, etc.)
Series D: 1 2 4 8 16 (multiply by 2)
Series E: 5 15 25 35 45 (odd multiples of 5)
Series F: 4 3 4 3 4 (down 1, up 1, down 1, up 1, etc.)
This MindBender was modified from a puzzle in Highlights "Puzzlemania," a good thinking resource for young kids.


September 10, 2001
MindBender
Crime
A crime has been committed, but the police don't know what the crime is or who did it. There are three suspects (A, B, and C), all with disreputable reputations. The suspects each make one true and two false statements. From their statements, can you determine what the crime was and who did it?
A's statements:
1. I stole a car.
2. B is innocent.
3. C is a disreputable person.
B's statements:
1. I robbed a service station.
2. I stole a car.
3. A is guilty.
C's statements:
1. I robbed a service station.
2. B's first statement is false.
3. A is innocent.
___________________________

Mini-MindBender for Kids
Silver Chain
You want to stay at a hotel in a foreign country and have no local currency to pay the innkeeper. You have a silver chain with seven links and the innkeeper agrees to accept one link as payment for each night and you want to stay seven nights. He wants to be paid each day. How can you handle this by cutting the fewest links in the chain?
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...Answer to MindBender
Crime

Consider that each suspect makes one true and two false statements. A's third statement is true. Therefore, A's first two statements are false. Therefore, B is guilty. Since A is innocent, C's third statement is true and his other statements are false. Therefore, B's first statement is true. So, B is guilty of robbing a service station. The summary true/false statement status is: A:FFT; B:TFF; C:FFT.

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
Silver Chain
Cut only the third link in the chain. This leaves you with three pieces of chain: 1, 2, and 4 links long. For the first night, pay with the 1-link chain. For the second night, give him the 2-link chain and take back the 1-link chain. For the third night, give him the 1-link chain. For the fourth night, give him the 4-link chain and take back the 1-link and 2-link chains. Handle the last three nights the same as the first three nights.
This MindBender was modified from a puzzle in "The Chicken from Minsk" by Yuri B. Chernyak and Robert M. Rose.


September 17, 2001
MindBender
Dragons
You are blind and encounter two talking dragons. Dragons can either be gray or red, and either meat-eaters or vegetarians. Gray vegetarians and red meat-eaters always tell the truth. Red vegetarians and gray meat-eaters always lie. The first dragon says: I am gray and the second dragon is a meat-eater. The second dragon says: the first dragon is a meat-eater and I am a vegetarian. What are the two dragons?
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Mini-MindBender for Kids
Four Words
The following four words share a common, interesting feature in their construction. Can you determine what that feature is? The words are: federation, conmoto, spontaneous, peanuts.
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...Answer to MindBender
Dragons

Since the first dragon says he is gray, he must be a gray vegetarian telling the truth, or a red vegetarian telling a lie. Therefore, the first dragon is a vegetarian. Therefore, the second dragon is telling a lie when he says the first dragon is a meat-eater. Therefore the second dragon is also lying when he says that he (the second dragon) is a vegetarian. So the second dragon is a meat-eater who tells lies. So the second dragon is a gray meat-eater. Therefore, from the first dragon's second statement, the first dragon is telling the truth and the first dragon must be a gray vegetarian. In summary, the first dragon is a gray vegetarian and the second dragon is a gray meat-eater.
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
Four Words
All four words have three consecutive letters of the alphabet backwards. FEDeration, cONMoto, sPONtaneous, peanUTS.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001


September 24, 2001
MindBender
Two Numbers
I ask you to pick an integer, positive or negative. Then I will name a number (maybe a fraction) such that the product of our two numbers equals your number minus twice my number. How can you keep me from accomplishing what I claim to be able to do?
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Mini-MindBender for Kids
Five Digits
Find a five digit number whose first two digits (read as a two digit number) are three times the third digit, and the last two digits (read as a two digit number) are twice the third digit. The sum of all the digits is 27.
___________________________
...Answer to MindBender
Two Numbers

Pick minus two (-2) as your number. Algebra shows us that the number I must pick is A/(A+2) where A is your number. If A is your number and B is my number, then we have:
A*B=A-2*B
A*B+2*B=A
B*(A+2)=A
B=A/(A+2)
Picking -2 means that I must divide by zero, which is not defined. Thus, I cannot name a number that works if you pick -2.
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
Five Digits
Even if we allow leading zeros in the answer, there are only 10 possible answers (1 for each possible third digit): 00000, 03102, 06204, 09306, 12408, 15510, 18612, 21714, 24816, and 27918. The all digit sum of 27 eliminates all but the last possibility. So the answer is 27918.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


October 1, 2001
MindBender
What Day
"L.T." Smith always lies on Mondays, Tuesdays, and Wednesdays. "L.T." always tells the truth on all other days. "L.T." makes the following two statements:
1. I lied yesterday.
2. I will lie again tomorrow.
What day of the week is it?
___________________________

Mini-MindBender for Kids
Missing Number
Find the number that completes the following sequence:
4 10 22 ?? 94
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...Answer to MindBender
What Day

If "L.T." is lying (i.e., it is Monday, Tuesday, or Wednesday), statement 1 means it is Monday. If "L.T." is telling the truth (it is Thursday, Friday, Saturday, or Sunday), statement 1 means it is Thursday.
Statement 2 is not possible if "L.T." is lying on Monday, but also not possible if "L.T." is telling the truth on Thursday. Therefore, there is no day of the week that "L.T." can make both of these statements.
This MindBender was modified from a puzzle in Raymond Smullyan's book, "What Is the Name of This Book."
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Answer to Mini-MindBender for Kids
Missing Number
The answer in the MindBender source and also the moderator's answer are the same: 46. However the source said to double the previous number and add 2 to get the current sequence entry. My answer said the differences between sequence elements were 6, 12, 24, 48, etc. Either reason (and maybe others) works for this sequence. It may also be possible that other reasoning may come up with a different, and equally valid answer.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


October 8, 2001
MindBender
Two Hustlers
Two hustlers are working a scam together. Five suspects have been identified. Each of the suspects makes a statement. The two guilty ones make false statements. The other three make true statements.
A: E is not one of the guilty ones.
B: C is not guilty.
C: D is innocent.
D: If B is not guilty, then A is guilty.
E: C is guilty.
Which two are the hustlers?
___________________________

Mini-MindBender for Kids
Running Race
Sarah was the 100th runner to finish the race. Many runners finished after Sarah. Here are some clues for the total number of runners who finished the race:
It is more than 280.
It is less than 316.
If you count by 4 from zero, you say its name.
It can be divided evenly by 7.
How many runners crossed the finish line?
___________________________
...Answer to MindBender
Two Hustlers

A and E are guilty. Assume that B is guilty. Then B's statement is false and C is also guilty. Then C's statement is false and D is also guilty. That is too many guilty people. Therefore, B is innocent. Then B's statement is true and C is not guilty. Then C's statement is true and D is not guilty. Therefore, A and E are the guilty parties. Further checking determines that A's statement and E's statement are indeed false, and D's statement is true, resulting in no conflict.
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
Running Race
Counting by 4 from zero is the same as being evenly divisible by 4. 280 is evenly divisible by 4 and by 7. But the number is larger than 280. The numbers divisible by 7 that are larger than 280 and smaller than 316 are: 287, 294, 301, 308, and 315. Of those numbers, only 308 is evenly divisible by 4. So, 308 runners finished the race.
This MindBender was modified from a puzzle in "The Problem Solver 4" by Judy Goodnow and Shirley Hoogeboom.


October 15, 2001
MindBender
Quick Calculation
Quickly now, what is 243**2 - 242**2 (i.e., 243 squared minus 242 squared)?
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Mini-MindBender for Kids
Relation
Alexander says: "If Dave's son is my son's father, what relation am I to Dave?"
___________________________
...Answer to MindBender
Quick Calculation

485 or 243+242. The difference between two consecutive squares is the sum of the numbers. This is because A**2-B**2=(A-B)*(A+B) and A-B=1.
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
Relation
Alexander is Dave's son since "my son's father" is Alexander.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


October 22, 2001
MindBender
Based Age
The MindBender is a day late this week because there was a birthday celebration yesterday. The MindBender moderator was 29 --- again! However, that 29 was base XX where XX is the product of two consecutive even numbers. Can you determine how old I really am?
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Mini-MindBender for Kids
Number Square
In the following number square, ask a friend to circle one number, and then cross out the other numbers in the circled number's row and column. Now have your friend circle another number and cross out the rest of its row and column. Now have your friend choose a third number and do the same thing again. Now is there a number left? Have your friend circle it also. Now have your friend add all the four circled numbers together. Before he shows you the sum, predict the answer is 56. Why does this work?
02 03 04 05
09 10 11 12
16 17 18 19
23 24 25 26
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...Answer to MindBender
Based Age

The base must be 4*6. A base of 2*4 or 8 would not allow a 9 as a digit. A base of 6*8 or 48 would make me 2*48+9=105 and I'm not that old. Any base larger than 6*8 would make me even older. So the base must be 4*6 or 24 and I am 2*24+9=57 years old. Obviously 57 is a very young number!
The MindBender moderator is the source for this MindBender.
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Answer to Mini-MindBender for Kids
Number Square
Your friend will always pick one number from each row and one number from each column. The sum then must be 2+9+16+23 (the column one sum) +1 (for the circled number from column 2) +2 (for the circled number from column 3) +3 (for the circled number from column 4). This is because each row's 2nd, 3rd, and 4th entries are one greater, two greater, and three greater than that row's 1st entry. This total will always be 56 (2+9+16+23+1+2+3).
This MindBender was modified from a puzzle in Highlights "Mathmania," a good thinking resource for young kids.


October 29, 2001
MindBender
Numbers
What are the origins of the following six numbers and the base number that connects them all?
31.41592
14.14213
17.32051
3,628,800
1024
59,049
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Mini-MindBender for Kids
Sequence
Find the number that completes the following sequence: 101 102 100 101 99 100 98 ?? 97 98
___________________________
...Answer to MindBender
Numbers

The base number is 10. The number origins are:
pi * 10
sqrt(2) * 10
sqrt(3) * 10
10!
2**10
3**10
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
Sequence
99. It can be viewed as two alternating sequences, both of which are decreasing by one. Or it can be viewed as a single sequence that adds 1, subtracts 2, adds 1, subtracts 2, etc. Other explanations and/or answers are also possible.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


November 5, 2001
MindBender
Thefts
Several thefts have occurred. The guilty party is one of three suspects. The suspects' statements are below. The guilty person's statement is false. The other two statements are true. Who is guilty?
A: C did it.
B: A's statement is false.
C: B's statement is true.
___________________________

Mini-MindBender for Kids
Some Sum
Determine the digits represented by A, B, C, and D in the following addition. A, B, C, and D are all different digits. 
 ABC 
 ABC 
 ABC 
_____ 
CDAB
___________________________
...Answer to MindBender
Thefts

If B's statement is false, C's statement must also be false. This is not allowed. So B is not guilty. If C's statement is false, B's statement must also be false. This is not allowed. So C is not guilty. If A's statement is false, B's statement is true and C's statement is also true. This all works. Therefore, A is guilty.
This MindBender was modified from a puzzle in Norman D. Willis' "The Little Giant Encyclopedia of Logic Puzzles."
___________________________

Answer to Mini-MindBender for Kids
Some Sum
Trying each of the possible values (1 to 9) for C leads to the following unique solution: 
 862 
 862 
 862 
_____ 
2586
The MindBender moderator is the source for this Mini-MindBender.


November 8, 2001
Midweek MindBender
Class
A school class has twice as many girls as boys. One of the boys has 7 more girl classmates than he has boy classmates. One of the girls has 5 more girl classmates than she has boy classmates. How many girls and how many boys are in the class?
___________________________

...Answer to Midweek MindBender
Class

There are 12 girls and 6 boys in the class.
This MindBender was modified from a puzzle in Dr. Abbie F. Salny's "The Mensa 365 Brain Puzzlers Calendar" for 2001.


November 12, 2001
MindBender
Secret Word
I have a secret word. It is one of the following five words: AIM DUE MOD OAT TIE. If I tell you any one letter of my secret word, you would be able to tell me the number of vowels in my secret word. What is my secret word?
___________________________

Mini-MindBender for Kids
Temperatures
Suppose that the average high temperature for the first 11 days of November is 47 degrees. If the high temperatures for the first 11 days of November are 56, 62, 69, 59, 60, 56, 46, 55, 64, 51, and 60, then how much warmer than average has it been?
___________________________
...Answer to MindBender
Secret Word

Consider the letters M, O, D. If I told you any one of those letters, then you could not determine the number of vowels in my secret word. Therefore, none of M, O, D can be in my secret word. This eliminates all words except TIE. So TIE is my secret word. Double checking TIE shows that any letter from TIE uniquely determines the number of vowels in the secret word. In other words, all words with T in them have 2 vowels; all words with I in them have 2 vowels; and all words with E in them have 2 vowels.
This MindBender was modified from a puzzle in George J. Summers' book, "The Great Book of Mind Teasers & Mind Puzzlers."
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Answer to Mini-MindBender for Kids
Temperatures
Add all the first 11 days' temperatures together and divide by 11. This gives us (56+62+69+59+60+56+46+55+64+51+60)/11=58 or 11 degrees warmer than average.
The MindBender moderator is the source for this Mini-MindBender.


November 14, 2001
Midweek MindBender
Party
As a party was coming to an end, 1/5 of the people left early. Later, 1/3 of the remaining guests left. Still later, 3/4 of those remaining left. This left two people still at the party. How many people were originally at the party?
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...Answer to Midweek MindBender
Party

15. When 1/5 left, 4/5 remained. When 1/3 left, 2/3 of 4/5 remained. When 3/4 left, 1/4 of 2/3 of 4/5 remained. 1/4 * 2/3 * 4/5 * X = 2. 8/60 * X = 2/15 * X = 2. So X = 15.
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2001.


November 19, 2001
MindBender
Products
Each of seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is a) represented by a different letter below; and b) positioned so that A*B*C = B*G*E = D*E*F. What digit does G represent? 
 A   D 
 B G E 
 C   F
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Mini-MindBender for Kids
Pounds of Dressing
Thanksgiving is Thursday this week in the United States. We will have a large group of people dining with us. Grampa loves dressing and will eat about 1/2 pound of it all by himself. The other 13 adults will average 1/4 pound of dressing each. Three of the 14 grandkids will not eat any. The other grandkids will average 1/8 pound each. How much dressing should the cooker prepare?
___________________________
...Answer to MindBender
Products

Since, at most, any letter is involved in two products, and since any number that is part of one product must have its factors part of each other product, no letter can be 0, 5, or 7. Since 9 = 3*3, it must be in two products and 3 and 6 must be in the other product. This gives us (for example, other possibilities are mirror images), E=9, A=6, and C=3. This leads to the following solution with other equivalent answers possible: 
 6   8 
 4 2 9 
 3   1
In all possible answers, G is the same. So, G is 2.
This MindBender was modified from a puzzle in George J. Summers' book, "The Great Book of Mind Teasers & Mind Puzzlers."
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Answer to Mini-MindBender for Kids
Pounds of Dressing
5 1/8 pounds. 1/2 + (1/4 * 13) + (1/8 * (14-3)) = 5 1/8 pounds. Hopefully the cooker will fix extra so there will be plenty of leftovers!
The MindBender moderator and his favorite cooker are the sources for this Mini-MindBender.


November 22, 2001
Midweek MindBender
Number
There is a number which, when added to 1 1/3, will give the same result as when it is multiplied by 1 1/3. What is that number?
___________________________

...Answer to Midweek MindBender
Number

The number is 4.
X + 4/3 = 4/3 * X
4/3 = 1/3 * X
X = 4
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


November 26, 2001
MindBender
Six Digit Addition
Each letter in this addition problem represents the same digit wherever it occurs. The digits used are 0, 2, 3, 4, 5, and 6. What digit is represented by each letter?

AEACA
EEABD
______
FCDCC
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Mini-MindBender for Kids
Stadium Entry
Bonnie is going to the stadium for a ball game. There are 12 different gates from the outside, and then there are 16 different stairways into the stadium. How many different ways can Bonnie go into the stadium?
___________________________
...Answer to MindBender
Six Digit Addition

From column 2, B=0 and there is no carry from column 1. Therefore, there is no carry to column 3. From column 1, A+D must be less than 7. So A must be less than 5. So, column 3 produces no carry and D=2*A. From column 1, C=3*A. So C=6. So A=2 and D=4. From columns 4 and 5, E=3 and F=5. The solution is:

23262
33204
______
56466
This MindBender was modified from a puzzle in Norman D. Willis' "The Little Giant Encyclopedia of Logic Puzzles."
___________________________

Answer to Mini-MindBender for Kids
Stadium Entry
192. For each gate you can pick one of 16 stairways. So, 12*16=192.
This MindBender was modified from a puzzle in "The Problem Solver 4" by Judy Goodnow and Shirley Hoogeboom.


November 29, 2001
Midweek MindBender
Some Number
If one third of some number is 1/17 of 1/5, what is that number?
___________________________

...Answer to Midweek MindBender
Some Number

3/85 Remember that "of" usually means to multiply, and "is" usually means equal. 
one third of some number is 1/17 of 1/5 
  1/3     *  X           =  1/17 *  1/5 
1/3 * X = 1/17 * 1/5 
1/3 * X = 1/85 
X = 3/85
This MindBender was modified from a puzzle in Terry Stickels' "Mindbending Puzzles" calendar for 2000.


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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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