potw50 - web viewthis genre of logic puzzles is baffling in large part because people rarely act...

7

Click here to load reader

Upload: vankien

Post on 14-Feb-2018

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

POTW50June 8, 2012 – 7:47 am

Four married couples, with names Albert, Bob, Charlie, Don, Elaine, Fanny, Gillian and Helen, meet for a game of chess. They form four groups of two players. The following information is given:(i) Bob plays against Elaine(ii) Albert plays against Charlie’s wife(iii) Fanny plays against Gillian’s husband(iv) Don plays against Albert’s wife.(v) Gillian plays against Elaine’s husband.

Who is Bob’s wife?

This is problem 4 from the 2001 SMO Junior Round 1.

Empat pasangan suami-isteri bernama Adi, Budi, Coki, Dodi, Eni, Fani, Gina dan Helen bertemu untuk bermain catur. Mereka membentuk empat grup dari dua orang dengan informasi berikut.

1) Budi bermain melawan Eni.2) Adi bermain melawan isteri Coki.3) Fani bermain melawan suami Gina.4) Dodi bermain melawan isteri Adi.5) Gina bermain melawan suami Eni.

Tentukan isteri Budi.

Dari lima informasi di atas, dapat ditarik kesimpulan sebagai berikut.1) Budi bermain melawan Eni.2) Adi bermain melawan isteri Coki.3) Fani bermain melawan suami Gina.4) Dodi bermain melawan isteri Adi.5) Gina bermain melawan suami Eni.

POTW134January 26, 2014 – 4:31 pm

Jane, June, Jean and Jenny are good friends. Something fascinating can be found mathematically with their names. Each letter of their name can be associated with an integer greater than 1 and the sum incidentally gives their current age. Jane is 16, June is a year older

Page 2: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

while Jenny is the oldest at 19. Suppose no two different letters are associated with the same integer. Which of the following number is a possible value for “u”?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

This is problem 14 from the 2003 SMO Junior Round 1.

POTW117September 14, 2013 – 8:35 am

Class A, with 15 students in the class, scored an average of 94 marks in a mathematics test. The maximum possible socre of the test is 100 marks. What is the lowest possible score that any of the 15 students could have scored?

This is problem 21 from the 1996 SMO Junior Round 1.

POTW116September 7, 2013 – 8:24 pm

On a plane, two men had a total of 135 kilograms of luggage. The first paid $12 for his excess luggage and the second paid $24 for his excess luggage. Had all the luggage belonged to one person, the excess luggage charge would have been $72. At most how many kilograms of luggage is each person permitted to bring on the plane free of additional charge?

This is problem 30 from the 1995 SMO Junior Round 1.

POTW76December 7, 2012 – 9:46 am

Two pipes can be used to fill up a swimming pool. The first can fill the pool in three hours, and the second can fill the pool in four hours. There is also a drain that can empty the pool in six hours. Both pipes were being used to fill the pool. After an hour, a careless maintenance man accidentally opened the drain. How long more will it take for the pool to fill?

This is problem 25 from the 1995 SMO Junior Round 1.

POTW45May 4, 2012 – 8:21 am

Three brothers, Peter, Paul and Jack, meet with their children in the family house. The children announce the following in turn:Isabelle: “I’m three years older than John”Theresa: “My father’s name is Jack.”Ivan: “I’m two years older than Isabelle.”Marie: “I’d rather play with one of my cousins that with my brother Frank.”Catherine: “My father’s name is Peter.”Ann: “I get along best with Uncle Jack’s sons.”

Page 3: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

John: “My father has fewer than four children.”Frank: “My father is the one with the least children.”

Which of the following statement is NOT correct?(A) Peter has three daughters.(B) Jack has two sons.(C) Marie and Frank have no other siblings.(D) Catherine and Isabelle are sisters.(E) Ann is Paul’s daughter.

This is problem 20 from the 2003 SMO Junior Round 1.

POTW43April 20, 2012 – 10:16 am

The ‘4’ button on my calculator is spoilt, so I cannot enter numbers which contain the digit 4. Moreover, my calculator does not display the digit 4 if 4 is part of an answer either. Thus I cannot enter the calculation   and do not attempt to do so. Also, the result of multiplying 3 by 18 is displayed as 5 instead of 54 and the result of multiplying 7 by 7 is displayed as 9 instead of 49. If I multiply a positive one-digit number by a positive two-digit number on my calculator and it displays 26, how many possibilities could I have multiplied?

This is problem 30 from the 2006 SMO Junior Round 1

POTW45May 4, 2012 – 8:21 am

Three brothers, Peter, Paul and Jack, meet with their children in the family house. The children announce the following in turn:Isabelle: “I’m three years older than John”Theresa: “My father’s name is Jack.”Ivan: “I’m two years older than Isabelle.”Marie: “I’d rather play with one of my cousins that with my brother Frank.”Catherine: “My father’s name is Peter.”Ann: “I get along best with Uncle Jack’s sons.”John: “My father has fewer than four children.”Frank: “My father is the one with the least children.”

Which of the following statement is NOT correct?(A) Peter has three daughters.(B) Jack has two sons.(C) Marie and Frank have no other siblings.(D) Catherine and Isabelle are sisters.(E) Ann is Paul’s daughter.

This is problem 20 from the 2003 SMO Junior Round 1

POTW60August 17, 2012 – 9:52 am

Page 4: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

Suppose that A,B,C are three teachers working in three different schools X,Y,Z and specializing in three different subjects: Mathematics, Latin and Music. It is known that(i) A does not teach Mathematics and B does not work in school Z;(ii) The teacher in school Z teaches Music;(iii) The teacher in school X does not teach Latin;(iv) B does not teach Mathematics.

Which of the following statement is correct?

1) B works in school X and C works in school Y;2) A teaches Latin and works in school Z;3) B teaches Latin and works in school Y;4) A teaches Music and C teaches Latin;5) None of the above.

POTW81January 11, 2013 – 9:04 am

Four people, A, B, C and D are accused in a trial. It is known that

if A is guilty, then B is guilty if B is guilty, then C is guilty or A is not guilty if D is not guilty, then A is guilty and C is not guilty if D is guilty, then A is guilty

How many of the accused are guilty?

i) 1 ii) 2 iii) 3 iv) 4 v) Insufficient information to determine.

This is problem 20 from the 2000 SMO Junior Round 1.

Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates:May 15, May 16, May 19June 17, June 18July 14, July 16August 14, August 15, August 17“My birthday is one of these,” she said.Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day. “Can you figure it out now?” she asked Albert.

Page 5: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.Bernard: I didn’t know originally, but now I do.Albert: Well, now I know, too!When is Cheryl’s birthday?

This genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful, for instance and no one gets offended and walks off when strangers insist on making basic communication so complicated. Students who compete in math competitions are generally familiar with the conventions of logic puzzles, but people who have not taken a math class for more than a decade generally say, “Huh?”

This puzzle is particularly convoluted. Why don’t Albert and Bernard just blurt out what Cheryl has told them? Why is Cheryl so coy about revealing the month and day, but not year, of her birthday? What else is Cheryl trying to hide?

But if you are willing to play, here’s how the logic unwinds.

It helps to put the list of 10 dates into table form:

Photo

Now let’s examine what Albert and Bernard say. Albert goes first:

I don’t know when your birthday is, but I know Bernard doesn’t know, either.

The first half of the sentence is obvious — Albert only knows the month, but not the day — but the second half is the first critical clue.

The initial reaction is, how could Bernard know? Cheryl only whispered the day, so how could he have more information than Albert? But if Cheryl had whispered “19,” then Bernard would indeed know the exact date — May 19 — because there is only one date with 19 in it. Similarly, if Cheryl had told Bernard, “18,” then Bernard would know Cheryl’s birthday was June 18.

Page 6: POTW50 -    Web viewThis genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful,

Thus, for this statement by Albert to be true means that Cheryl did not say to Albert, “May” or “June.” (Again, for logic puzzles, the possibility that Albert is lying or confused is off the table.) Then Bernard replies:

I didn’t know originally, but now I do.

So from Albert’s statement, Bernard now also knows that Cheryl’s birthday is not in May or June, eliminating half of the possibilities, leaving July 14, July 16, Aug. 14, Aug. 15 and Aug. 17. But Bernard now knows. If Cheryl had told him “14,” he would not know, because there would still be two possibilities: July 14 and Aug. 14. Thus we know the day is not the 14th.

Now there are only three possibilities left: July 16, Aug. 15 and Aug. 17. Albert again:

Well, now I know too!

The same logical process again: For Albert to know, the month has to be July, because if Cheryl had told him, “August,” then he would still have two possibilities: Aug. 15 and Aug. 17.

The answer is July 16.

Cheryl is a Cancer, which still does not explain her behavior.

If you want it broken down another way, The Guardian also explained it.

Disagree? Got a question? Write a comment.

If you had fun and would like to try more (harder!) math puzzles, check out The Times’ Numberplay blog.