akpsi charity brainteaser competition

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?


QUESTION 1- 1 minute

If 10 people, on parting, all shake hands with each other once,

how many handshakes will there be altogether?



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?



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) = ___


QUESTION 4- 3 minutes

Rearrange the letters in the words “new door”

using each letter, to make one word.



The top two scales are in perfect balance. How many

diamonds will be needed to balance the bottom set?



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?



Here is a series of numbers What is the next number in the sequence?

1

11

21

1211

111221

312211

13112221

…?



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?



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?



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?



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?



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- ____



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.



What number should be placed inside the last triangle?



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?



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.



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)?



What is the average number of flips on a fair coin it takes to

get two heads in a row?



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?


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.


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.


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


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.


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.


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”


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.


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.


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…


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.


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.


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


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


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.


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


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


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


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.


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


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


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


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.


FINAL QUESTION

akpsi charity brainteaser competition

Documents

booth doubles

passing day

bee travel

minutestwo trains

supersonic bee

bee surviving

dark bridge

minutesfour men m1