1. No calculators.
2. Computers and/or phones with internet access may not be used at any time.
3. No team members may be added after the start of the competition.
4. All decisions regarding the correctness of an answer are final.
5. No consulting with other teams to answer a brainteaser.
6. There are 20 questions, each worth a point.
7. The top three teams will enter the final round.
8. Have fun!
CHARITY BRAINTEASER COMPETITION 2011
RULES
You are building a booth for carnival with your friends in such
a way that with each passing day the booth doubles in
progress. If you finish the booth in 8 days, on which day will
the booth be a quarter of the way done?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 1- 1 minute
If 10 people, on parting, all shake hands with each other once,
how many handshakes will there be altogether?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 2- 1 minute
A snail is at the bottom of the 80-foot-long “Walking to the Sky”
statue and decides to make his way to the top. He climbs up 3
feet each day, but then slips back 2 feet during his night-time
slumber. How long does it take the snail to get to the top?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 3- 1 minute
Three men, A, B and C, toss a fair coin in succession. The
winner will be the first to throw a head. What are their
respective chances of winning?
P(A winning) = ___
P(B winning) = ___
P(C winning) = ___
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 4- 3 minutes
Rearrange the letters in the words “new door”
using each letter, to make one word.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 5- 2 minutes
The top two scales are in perfect balance. How many
diamonds will be needed to balance the bottom set?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 6- 3 minutes
Two trains enter a tunnel 200 miles long traveling at 100 mph at the same time from opposite directions. As soon as they enter the tunnel a supersonic bee flying at 1000 mph starts from one train and heads toward the other one. As soon as it reaches the other one it turns around and heads back toward the first, going back and forth between the trains until the trains collide in a fiery explosion in the middle of the tunnel, with the bee surviving.
How far did the bee travel?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 7- 2 minutes
Here is a series of numbers What is the next number in the sequence?
1
11
21
1211
111221
312211
13112221
…?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 8- 2 minutes
Four men- M1, M2, M3 and M4 and four ladies- L1, L2, L3 and L4 are very fond of chess. One day after they had played one game each, it was observed that
a) Though L2 and L3 both lost, ladies won more games than men
b) M2 won his game, but M3 lost.
Who did M1 play with?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 9- 3 minutes
Of the 100 CMU students at a recent party, 90 majored in
engineering, 80 majored in mathematics and 75 majored in
business. At least how many majored in all three?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 10- 3 minutes
Father, mother, son and daughter need to cross a dark bridge.
They have only one torch and only 2 persons can be at the
bridge at any time. Mother can cross bridge in 10 mins,
father in 5, daughter in 2 and son in 1. What is the minimum
time needed?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 11- 3 minutes
The probability of seeing a shooting star in Pittsburgh over
the next hour is .84. What is the chance of seeing a shooting
star in the next half hour?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 12- 2 minutes
There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow,
and 2 pairs of green. You select the gloves in the dark and can check
them only after a selection has been made. What is the smallest
number of gloves you need to select to have at least one matching pair
(left and right hands, same color) in the best case? In the worst case?
Best- ____
Worst- ____
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 13- 3 minutes
Mr. Baker, Mr. Cyert, and Mr. Doherty once were all on a conference call as each were located in a CMU building- baker, cyert, or doherty. They each knew what building each was located at. Did you notice, said Mr. Doherty, “we are sitting in buildings that match our names, but none of us is in a building with the same title as our name?” “You are very observant, said the person in cyert.
Match the names and buildings.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 14- 3 minutes
What number should be placed inside the last triangle?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 15- 3 minutes
I am nine letters long- 123456789
My 123 is a mischief
My 3456 is to the left
My 678 is a shade of brown
My 789 is a social insect
What am I?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 16- 3 minutes
I tell you that I have two children and that one of them is a
girl (I say nothing about the other). What is the probability
that I have two girls? Assume that boys and girls are equally
likely to be born and that the gender of one child is
independent of gender of another.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 17- 2 minutes
Picture the CMU cut as a grid. You start at coordinate (0,0)
and move one step at a time, eventually arriving at coordinate
(4, 3). With each step you may move only one step east or
one step north but never diagonally. How many paths are
there from (0,0) to (4, 3)?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 18- 3 minutes
What is the average number of flips on a fair coin it takes to
get two heads in a row?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 19- 4 minutes
Precisely when the big (minute) hand of the clock passes 12, an ant begins crawling counterclockwise around the clock from the mark 6 at a consistent speed. When reaching the big hand of the clock, the ant turns around and, at the same speed, starts marching around the clock in the opposite direction. Exactly 45 minutes after the first meeting, the ant crosses the big hand for the second time.
How long has the ant been walking?
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 20-5 minutes
Six CMU professors sat around a table discussing their ages. Those who were 40 years of
age and older were truthful unless their ages were a multiple of 17; those who were
under 40 years of age lied unless their ages were divisible by 13. None of the professors
was over 70 years old. The total of their ages was 261.
Each professor said: 1. Number 5 is older than I am.
2. Number 1 is 30 years younger than Number 3.
3. I am 51.
4. Number 3 is 52. I am not 29.
5. Number 1 is a liar.
How old were they? 6. Number 4 is wrong. Number 2 is 39.
CHARITY BRAINTEASER COMPETITION 2011
FINAL QUESTION
You and your friends are building a blitz booth for carnival in such a way that with each passing day the booth progress doubles in size. If you finish the booth in 8 days, on which day will the booth be a quarter of the way done?
Answer: 6 days6 days6 days6 days
On day 7, the booth will be a half of the way done.
On day 6, the booth will be a quarter of the way done.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 1
If 10 people, on parting, all shake hands with each other once, how many handshakes will there be altogether?
Answer: 45 45 45 45
9+8+7+…+3+2+1, or 10 choose 2
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 2
A snail is at the bottom of the 80-foot-long “Walking to the Sky” statue decides to make his way to the top. He climbs up 3 feet each day, but then slips back 2 feet during his night-time slumber. How long does it take the snail to get to the top?
Answer: 78 days78 days78 days78 days
After 77 days, the snail will be at 77 feet. On the 78th day the
snail will climb 3 feet in the day, reaching the top.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 3
Three men, A, B and C, toss a fair coin in succession. The winner will be the first to throw a head. What are their respective chances of winning?
Answer:
P(A winning) = 4/74/74/74/7
P(B winning) = 2/72/72/72/7
P(C winning) = 1/71/71/71/7
Because A goes first, he has twice the chance that B has. Because B goes second, he has twice the chance that C has- therefore 4 to 2 to 1.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 4
Rearrange the letters in the words “new door”, using each letter, to make one word.
Answer: “one word”“one word”“one word”“one word”
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 5
The top two scales are in perfect balance. How many diamonds will be needed to balance the bottom set?
Answer: 4 diamonds4 diamonds4 diamonds4 diamonds
Add the first two scales together.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 6
Two trains enter a tunnel 200 miles long traveling at 100 mph at the same time from opposite directions. As soon as they enter the tunnel a supersonic bee flying at 1000 mph starts from one train and heads toward the other one. As soon as it reaches the other one it turns around and heads back toward the first, going back and forth between the trains until the trains collide in a fiery explosion in the middle of the tunnel , with the bee surviving.
How far did the bee travel?
1000 miles 1000 miles 1000 miles 1000 miles
The tunnel is 200 miles long, the trains meet in the middle traveling at 100 mph, and so it takes them an hour to reach the middle. The bee travels at 1000 mph for an hour, which covers 1000 miles.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 7
Here is a series of numbers What is the next number in the sequence?
1
11
21
1211
111221
312211
13112221
…?
Answer: 1113213211111321321111132132111113213211
Each number describes the previous number.
For example- you start with 1, which is simply one 1, so the
next number is 11. Now you have two 1’s, so the next
number is 21. Now you have one 2 and one 1, so the next
number is 1211…
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 8
Four men- M1, M2, M3 and M4 and four ladies- L1, L2, L3 and L4 are very fond of chess. One day after they had played one game each, it was observed thata) Though L2 and L3 both lost, ladies won more games than menb) M2 won his game, but M3 lost.
Who did M1 play with?
Answer: M4M4M4M4.
There were at least 3 games which were not drawn, so ladies won two games, men one and the third was a draw. Ladies won two and lost two, so none were involved in a draw. M2 won, M3 lost. So M1 played M4 to a draw.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 9
Of the 100 CMU students at a recent party, 90 majored in engineering, 80 majored in mathematics and 75 majored in business. At least how many majored in all three?
Answer: 45454545
10 are not engineering, 20 are not mathematics, and 25 are not business
The problem asks “at least” how many- must assume that these 10, 20, and 25 people are all separate people. Having identified 55 each of whom is missing one major, the remaining 45 major in all three.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 10
Father, mother, son and daughter need to cross a dark bridge. They have only one torch and only 2 persons can be at the bridge at any time. Mother can cross bridge in 10 mins, father in 5, daughter in 2 and son in 1. What is the minimum time needed?
Answer: 17 mins17 mins17 mins17 mins
(2+1+10+2+2) or (2+2+10+1+2)
The trick is to group the mother and father in one crossing
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 11
The probability of seeing a shooting star in Pittsburgh over the next hour is .84. What is the chance of seeing a shooting star in the next half hour?
Answer: 60%60%60%60%
(1-.84)^(1/2) = .40
1 - .4 = .6
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 12
There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the dark and can check them only after a selection has been made. What is the smallest number of gloves you need to select to have at least one matching pair in the best case? In the worst case?
Answer: 12 and 212 and 212 and 212 and 2
The worst case number, 12, is one more than the number of gloves of one handedness.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 13
Mr. Baker, Mr. Cyert, and Mr. Doherty once were all on a conference call as each were located in a CMU building- baker, cyert, or doherty. Did you notice, said Mr. Doherty, “we are sitting in buildings that match our names, but none of us is in a building with the same title as our name?” “You are very observant, said the person in cyert.
Match the buildings and names.
Answer:
Mr. Doherty Mr. Doherty Mr. Doherty Mr. Doherty –––– baker baker baker baker Mr. Cyert Mr. Cyert Mr. Cyert Mr. Cyert –––– dohertydohertydohertydoherty Mr. Baker Mr. Baker Mr. Baker Mr. Baker –––– cyertcyertcyertcyert
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 14
What number should be placed inside the last triangle?
Answer: 3333
The top number minus the bottom left-hand number is
multiplied by the bottom right-hand number to give the
number inside the triangle
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 15
I am nine letters long- 123456789
My 123 is a mischief
My 3456 is to the left
My 678 is a shade of brown
My 789 is a social insect
What am I?
Answer: ImportantImportantImportantImportant
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 16
I tell you that I have two children and that one of them is a girl (I say nothing about the other). What is the probability that I have two girls? Assume that boys and girls are equally likely to be born and that the gender of one child is independent of gender of another.
Answer: 1/31/31/31/3
You know only that I have two children and that one is a girl. Without knowing that, there are four possible equally outcomes: GG, GB, BG, BB. With that information, the last outcome is excluded. The probability of GG out of GG, GB, BG is 1/3.
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 17
Picture the CMU cut as a grid. You start at coordinate (0,0) and move one step at a time, eventually arriving at coordinate (4.3). With each step you may move only one step east or one step north but never diagonally. How many paths are there from (0,0) to (4,3)?
Answer: 35 ways35 ways35 ways35 ways
You will take a total of seven steps. Four of these will be east; three will be north. You can either choose which four of the seven are east, or which three are north. (7 choose 4) = (7 choose 3) = 7!/(4!*3!)= 35 ways
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 18
What is the average number of flips on a fair coin it takes to get two heads in a row?
Answer: 6666
Let x = your answer
x = (1/2)(Tails) + (1/2)(Heads)
= (1/2)(x + 1) + (1/4)(Heads, Heads) + (1/4)(Heads, Tails)
= (1/2)(x + 1) + (1/4)(2) + (1/4)(x + 2)
x = 6
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 19
Precisely when the big (minute) hand of the clock passes 12, an ant begins crawling counterclockwise around the clock from the mark 6 at a consistent speed. When reaching the big hand of the clock, the ant turns around and, at the same speed, starts marching around the clock in the opposite direction. Exactly 45 minutes after the first meeting, the ant crosses the big hand for the second time. How long has the ant been walking?
Answer: 54 minutes54 minutes54 minutes54 minutes
As the big hand covers ¾ of a revolution (45 minutes), the ant has to cover 1 ¾ revolutions � ratio of 1.75: 0.75 = 7:3.
At the beginning the big hand covered 3/10ths of thirty minutes = 9 minutes
The ant traveled 9 + 45 = 54 minutes
CHARITY BRAINTEASER COMPETITION 2011
QUESTION 20
How old were they? 1111---- 38383838
2222---- 39393939
3333---- 68686868
4444---- 29292929
5555---- 26262626
6666---- 61616161
Congratulations to our winners! Thanks, and see you all next year.
CHARITY BRAINTEASER COMPETITION 2011
FINAL QUESTION
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