Can you solve these brain teasers?

Can you solve these brain teasers?

By now, everyone knows how difficult it is to figure out when Cheryl's birthday is.

Yes, it is that mathematics problem from a Secondary 3 Math Olympiad question.

Just to see how tough the questions could be, The New Paper on Sunday put together a set of similar questions from the Singapore Mathematical Olympiad and put three people to the test.

Q1) 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?

Q2) 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?

Q3) 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 one and the sum incidentally gives their current age. Jane is 16, June is a year older while Jenny is the oldest at 19. Suppose no two different letters are associated with the same integer.

Which of the following numbers is a possible value for "u"?

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

*These questions are from the 2001, 1995 and 2003 Singapore Mathematical Olympiad (SMO) Junior Round 1 respectively.

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